Angles in triangles and quadrilaterals worksheet

I am a beginner to OpenFOAM 11 so apologies in advance if this is a simple question.
So I am trying to simulate a wind tunnel test of an aircraft and I am currently trying to mesh using snappyHexMesh. My process that I am following is creating a poor mesh using blockMesh, then refining that mesh using snappy. The geometry is basically a wind tunnel (box) and the aircraft is inside of it.
I built the blockMesh file such that I mesh the wind tunnel (no aircraft is mentioned in the blockMesh), and then I refine the mesh of the tunnel and add refinements for the aircraft as well in the snappy. The issue I am facing is that after snappy is ran (with no errors) and I go to the polymesh folder, in the boundary file I can only see that the tunnel is meshed, nothing about the aircraft is mentioned. So I am starting to think that maybe I should have mentioned the aircraft in the blockMesh as well? Although that's not the impression I got when reading the documentation so I am confused a bit. Here is my blockMeshDict:

FoamFile { version 2.0; format ascii; class dictionary; object blockMeshDict; } convertToMeters 1; vertices ( (-0.5 -0.884 0.9675) // vertex 0 (-0.5 -0.884 -0.9675) // vertex 1 (-0.5 0.884 -0.9675) // vertex 2 (-0.5 0.884 0.9675) // vertex 3 (2 -0.884 0.9675) // vertex 4 (2 -0.884 -0.9675) // vertex 5 (2 0.884 -0.9675) // vertex 6 (2 0.884 0.9675) // vertex 7 ); blocks ( hex (0 1 2 3 4 5 6 7) (50 25 25) simpleGrading (1 1 1) // Coarser mesh ); edges ( ); boundary ( bleeding { type patch; faces ( (0 3 4 7) // Bottom face of the tunnel (1 2 5 6) // Top face of the tunnel ); } walls { type wall; faces ( (0 1 4 5) // right face of the tunnel (2 3 6 7) // left face of the tunnel ); } inlet { type patch; faces ( (0 1 2 3) // inlet of the tunnel ); } outlet { type patch; faces ( (4 5 6 7) // outlet of the tunnel ); } ); mergePatchPairs ( ); 

And this is my snappyHexMeshDict file:

FoamFile { version 2.0; format ascii; class dictionary; object snappyHexMeshDict; } castellatedMesh true; snap true; addLayers true; geometry { TRY_body_scaled.stl { type triSurfaceMesh; name body; } TRY_fin1_scaled.stl { type triSurfaceMesh; name fin1; } TRY_fin2_scaled.stl { type triSurfaceMesh; name fin2; } TRY_fin3_scaled.stl { type triSurfaceMesh; name fin3; } TRY_fin4_scaled.stl { type triSurfaceMesh; name fin4; } TRY_fin5_scaled.stl { type triSurfaceMesh; name fin5; } TRY_fin6_scaled.stl { type triSurfaceMesh; name fin6; } TRY_fin7_scaled.stl { type triSurfaceMesh; name fin7; } TRY_fin8_scaled.stl { type triSurfaceMesh; name fin8; } TRY_tunnel_scaled.stl { type triSurfaceMesh; name tunnel; } } castellatedMeshControls { maxLocalCells 1000000; maxGlobalCells 4000000; minRefinementCells 10; maxLoadUnbalance 0.10; nCellsBetweenLevels 3; allowFreeStandingZoneFaces true; features ( ); refinementSurfaces { body { level (3 4); } fin1 { level (2 3); } fin2 { level (2 3); } fin3 { level (2 3); } fin4 { level (2 3); } fin5 { level (2 3); } fin6 { level (2 3); } fin7 { level (2 3); } fin8 { level (2 3); } tunnel { level (1 2); } } resolveFeatureAngle 30; refinementRegions { body { mode outside; levels ((1E15 3)); } fin1 { mode outside; levels ((1E15 2)); } fin2 { mode outside; levels ((1E15 2)); } fin3 { mode outside; levels ((1E15 2)); } fin4 { mode outside; levels ((1E15 2)); } fin5 { mode outside; levels ((1E15 2)); } fin6 { mode outside; levels ((1E15 2)); } fin7 { mode outside; levels ((1E15 2)); } fin8 { mode outside; levels ((1E15 2)); } tunnel { mode inside; levels ((1E15 1)); } } locationInMesh (0 0 0); } snapControls { nSmoothPatch 3; tolerance 2.0; nSolveIter 30; nRelaxIter 5; } addLayersControls { relativeSizes true; layers { body { nSurfaceLayers 2; // Reduce the number of layers } fin1 { nSurfaceLayers 2; } fin2 { nSurfaceLayers 2; } fin3 { nSurfaceLayers 2; } fin4 { nSurfaceLayers 2; } fin5 { nSurfaceLayers 2; } fin6 { nSurfaceLayers 2; } fin7 { nSurfaceLayers 2; } fin8 { nSurfaceLayers 2; } } expansionRatio 1.2; finalLayerThickness 0.2; minThickness 0.1; nGrow 0; featureAngle 30; slipFeatureAngle 30; nRelaxIter 5; nSmoothSurfaceNormals 1; nSmoothNormals 3; nSmoothThickness 10; maxFaceThicknessRatio 0.5; maxThicknessToMedialRatio 0.3; minMedianAxisAngle 90; nBufferCellsNoExtrude 0; nLayerIter 50; nRelaxedIter 20; } meshQualityControls { maxNonOrtho 70; // Increase from 65 to 70 maxBoundarySkewness 25; // Increase from 20 to 25 maxInternalSkewness 5; // Increase from 4 to 5 maxConcave 85; // Increase from 80 to 85 minVol 1e-14; // Decrease from 1e-13 to 1e-14 minTetQuality 1e-10; // Decrease from 1e-9 to 1e-10 minArea -1; minTwist 0.02; // Decrease from 0.05 to 0.02 minDeterminant 0.0001; // Decrease from 0.001 to 0.0001 minFaceWeight 0.02; // Decrease from 0.05 to 0.02 minVolRatio 0.001; // Decrease from 0.01 to 0.001 minTriangleTwist -1; nSmoothScale 4; errorReduction 0.75; } debug 0; mergeTolerance 1e-6; 

First/Previous
"Watch out!" Jack yelled out to the crowd as the now-glowing overhead turrets, long dormant and forgotten, suddenly whirred to life with a mechanical hum, tracking his movements as he ran, shoving past a group of unsuspecting Xarak to the side as he moved to dodge the torrent of rapid fire aimed right at him, kicking up smoke as the superheated plasma churned the ground underneath him, before the sound of gunfire abruptly stopped.
"Fucking overheating shittubes!" the voice on the speakers cursed. "The Outsider is by the two broken pillars!"
"I see him!" a voice replied from out of the crowd as Jack got his bearings, spotting a group of three uniformed soldiers rushing towards him. As the leader moved to stab him with a nasty-looking barbed shortspear, Jack quickly juked the direction he intended to dodge, dipping to the right as he smashed the avian in the stomach with a vicious kick, shuffling back as he caught the blade of the second soldier with his bracer before throwing them off balance, lashing back at the first with his elbow as he did.
He moved to check the third that was moving to take a swing at him with a bat, but before Jack could do so the soldier was suddenly yanked back as a long, coiled leather whip snapped around them. Following along, Jack spotted an older grey-skinned ganger in black leathers with a coarse, black beard to match his scraggly hair sat down with his back to a wall, casually drinking a beer as he observed the chaos with a mischievous smirk.
As the soldier pulled back his bat to strike the interloper, the ganger grinned and looked down where his legs were already spread wide, revealing a strange metal crotch plate. Suddenly making a jerking motion with one of his legs, the plate flipped up to reveal the barrel of a huge codpiece gun that flipped up to point directly at the soldier, before it fired once, catching the solder completely by surprise as the top of their body was utterly obliterated by a bolt of powerful plasma energy. Smirking, the ganger gave Jack a wink, chugging down the rest of his drink, before charging into the brawl.
Hearing an almighty roar, Jack turned around only to be knocked back yet again as a broken, avian body was roughly lobbed at him, staggering him backwards as the Redeemer turned to the last of the bird-like gangsters, picking him up with immense strength and smashing them to the ground before advancing towards the human more cautiously this time, shoving drunken brawlers out of the way.
“I have long waited for this moment, Outsider. With your death, my King shall grant you redemption!” The Redeemer snarled. Now having a good look at him, Jack couldn’t see any visible weapons on him, which was strange. Last time, he’d brought a gunship and was taking potshots at him with some kind of high-powered rifle. Then again, considering what happened last time, maybe The Redeemer wanted the satisfaction of using his bare hands to beat him to death.
It wouldn’t be a terrible plan considering everything the Ogar had pulled off so far…
While sports on Earth were often separated by gender, despite some resistance from the more liberal-minded, due to biological differences between men and women, combat sports were a whole different game, with mixed martial arts organisations having very specific weight classes for fair competition between athletes, with two fighters of similar size and weight less likely to cause serious injury to each other.
But if you placed an experienced lightweight against even a novice heavyweight? That would introduce major problems for the smaller fighter, who would need to contend with the extra size, reach and power of their larger opponent. Not an impossible fight, but a tough one.
And Jack very much felt like a lightweight here.
Though of course, he had faced larger opponents before. Even an Ogar, though they had defeated the Laird with a cunning trap. However, he didn’t know how well matched he and The Redeemer were in a fair close-range fight outside of the opening moments of the ambush.
Still, he had little choice but to find out. He didn’t have an easy way to escape, and he didn’t know what the status of the others was. If he ran while they were still here then The Redeemer and the Regulators would simply go after them instead to get to him…
No. He couldn’t allow those thoughts to shake him. His friends knew what the hell they were doing, and they could handle themselves just fine. He had to worry about himself right now.
He couldn’t run, so he had to fight.
With a speed he didn’t expect from The Redeemer, they grabbed a nearby chair and lobbed it right at Jack in one smooth motion before following through with another charge.
‘Aegis!’ Jack yelled as he brought his forearm up, as his new and improved shield eagerly sprung up to take the hit from the chair, before a fist smacked into the side of his head as The Redeemer used the chair as a distraction to change his angle of attack.
Spinning with the blow, Jack fought in his mind to stay in the fight as his vision blurred, with the powerful strike threatening to knock him out then and there, before another fist caught him in the stomach, with his battleskin dispersing a hit that would have otherwise easily taken the air out of his lungs.
Retracting his shield, Jack ducked another punch that threatened to decapitate him as he skidded under the blow, parrying a backfist with his forearm that tingled painfully as he ate the blow, before clocking the Redeemer with a punch to the jaw, his gauntlet extending to cover his knuckles with a well-forged plate of metal to add their power to the strike, before the Redeemer threw out a punch that caught him on the shoulder, sending the deathworlder reeling back.
Jack grit his teeth as he fought through the pain, adrenaline rushing through him. He wasn’t out of the fight yet, but he knew he’d gotten the worst of that engagement.
The Redeemer clearly understood this as well, as the zealot strode towards the human with a confident, wicked grin.
But this time, Jack was ready.
‘Caltrops’ Jack whispered the command word, as his gauntlets gave him a good handful of them, subtly tossing them in front of him with an underhand throw, which had gone unnoticed by the Redeemer as they stared at the human with hatred.
Suddenly dashing forward to quickly close the remaining distance between them, the Redeemer roared as he charged Jack again, suddenly grunting in pain and stumbling as his full, heavy mass sent a sharp, painful spike straight through his armoured boot, causing him to lose focus as he looked down at his foot for just a moment to see what had happened.
A moment of distraction that Jack used to its fullest, as he quickly swung his axe down right at The Redeemer’s head.
However, the Ogar reacted with surprising dexterity as he used his forward momentum to avoid the full force of the axeblade, his metal helmet taking a glancing blow as he shoved Jack off balance, causing him to stumble. Quickly predicting what would come next, Jack dropped his axe on purpose as he prepared for a takedown attempt, dropping low and widening his stance as the Redeemer tackled him around the waist to try and bring him to the ground for a quick finish.
“There will be no salvation for you, human!” The Ogar growled through his pain as Jack was forced back by the Redeemer’s superior strength.
“Aww, did you miss me?” Jack taunted, holding on and walking back with the ever increasing momentum The Redeemer was building as he was pushed back along the dancefloor. “I saw your tantrum on the TV afterwards, didn’t know you were a bitch too!”
‘That’s it, asshole.’ Jack thought to himself as he felt his axe clip back onto his back. ‘Get mad. You showed me last time that you like to talk too much. I need to time this right…'
“Your blasphemy ends here Outsider! I shall smite you in the name of my King!” The insane zealot roared out in an enraged challenge.
With a roar the Redeemer pushed with much greater strength, forcing Jack to change his slow backpedalling into a full on sprint as he scrambled to stay on his feet, fighting to keep his grip above that of the Redeemer’s to maintain his control of the grapple for as long as he could as he was gradually being put off-balance, almost being lifted upwards.
‘I’ve got to hold on until the last possible moment…’ Jack thought to himself, as tables, chairs and people alike were battered to the side.
‘Now!’
As the wooden pillar supporting the balcony passed them in a blur, Jack shifted his weight to the left and relinquished the grapple, using the Redeemer’s momentum against him as he shoved the Redeemer off balance, as they smashed into the crumbling brick wall head first with an almighty crash.
As they stumbled back, yanking their head back out through the newly formed hole, Jack growled as grabbed the Redeemer around the top of one of his legs, yelling with effort as he was only just able to lift the Redeemer up and over him, slamming the Ogar down on the top of his head as hard as he could in a vicious suplex that gave a satisfying crack.
Growling with effort, the Redeemer pushed himself back into a crouch and looked up just in time as Jack’s foot smacked into the side of his head in a savage kick that cracked his metal helmet and dislodged one of his fangs. Roaring in rage and pain, the Redeemer got to his feet only to meet a flying knee that shattered his nose as his helmet cracked and dented with the heavy impacts.
“Redeem that you ugly cunt!” Jack growled, moving in for another strike as the Redeemer shoved him away, showing no signs of faltering as he slowly got to his feet, even after the devastating blows he just took. The Redeemer simply gave Jack a wicked grin of satisfaction, before it fell slightly upon seeing something to Jack’s side.
As Jack’s Ring of the Berserker vibrated again, he spun around to spot a large, lanky Vivren with several piercings in overt heavy armour grinning at him with malicious intent as she pointed a wand at him and cast a word of power.
Before he had any time to react, Jack’s entire body erupted in a wave of agony unlike anything he had ever felt before…
*****
“Fuck! Alora! Sephy? Chiyo? Dante?” Nika coughed as she got up from where the balcony had collapsed from under them.
Looking around, she could see even more patrons fighting around them, revelling in the chaos of the brawl, but she couldn’t spot any of her friends in the immediate aftermath, as thick dust plumed out from the wreckage below her.
‘At least the crew of the ship we’re meant to be travelling on are probably out by now.’ The Kizun thought to herself. ‘Can’t go back, the CorvMart crew will have moved on by now, so sticking to the original plan is probably the best move, unless we can steal a vehicle one of us knows how to pilot.’
Assessing the situation before her, Nika went for her bo staff, though made sure that her shotgun was well within easy reach. Though many of the people fighting around her looked rough, they weren’t attacking her or her friends, and until that changed they could make good allies of convenience, or for a smokescreen to give their enemies the slip if they had to run.
Though slaying as many of their attackers as they could would be preferable.
‘Best way to do that is link up with the others, we’re better as a unit.’ She reasoned, hearing an almighty crash. ‘Well, that’s probably Jack.’
Dodging a thrown bottle as a Squarri ganger missed their intended target - a pissed-off looking quadrupedal furry species that Nika didn’t recognise - before dodging a swing of a bat from a Xarak that saw her as an easy target. Quickly raising her staff she parried the backswing before cracking the other end of the staff across the reptilian’s face, knocking the rough-looking thug out as he collapsed to the ground.
Yet before Nika could think to move on from the conflict, she had to dodge out of the way using her tail as a large Balnath with some kind of cleaver-like sword took a swing at her. Recognising the sigil of the Regulator group Chiyo had told them to watch out for - a stern-looking demonic rune surrounded by a neon-red triangle - Nika parried the next sword swipe from the figure.
“Let me guesth, you want to get to the Outthider?” The Balnath sneered at the Kizun with a lisp so thick that in any other situation she’d have to stop herself from laughing. “I’m stho thorry, but we can’t let you have sthilly ideas like that!”
“Are you for fucking real?” Nika asked as she dodged to the side and put some space between them before quickly switching to her shotgun, letting loose a powerful blast that the Balnath was able to raise his shield up to block.
‘Skill like that? Probably the leader or an officer of some kind.’ The Kizun noted to herself. ‘No choice. I’ve got to kill him.’
“Yeah, I know that you’re finking! You fink my teef make me sound sthupid?” The Balnath growled, with a few experimental chomps. “Well these teef like to gnaw and gnasth on Kizun flesth!”
“Come and try it!” Nika snarled as she twirled her staff around her in a well-practised flourish, eagerly accepting the challenge.
The Balnath charged forward with lightning speed as it came at Nika with a series of feints, before swiping at her with a brutal overhand chop, using both hands. The Kizun was able to deftly parry with her staff, the kinetic modules battering her opponent’s grip to the side, though she felt the strength behind the blow and knew that the Balnath was stronger.
Still, she knew she could take him.
Ever since she was little she had roughhoused with her brothers and the local boys in fights around their ranch, and had learned the hard way from an early age that her gender and short build worked against her when facing her peers, so she had trained to be the strongest she could be, and learned to be quick and tactical to make the best use of that.
She had eventually kept up with the neighbourhood boys, using holds and precise strikes until her elders found out what she was doing when she was meant to be working on the ranch to help the family scrape by, and quickly put a stop to the shenanigans.
When she moved to the city, she only got better from there.
The tip of her staff thundered against the Balnath’s shield like the striking of a gong, forcing the larger being back as Nika could tell he was already tiring. Though she wanted to finish this fight quickly and get to her friends, she knew she couldn’t allow herself to give her opponent an opening, even as she sought to exploit an opening of her own. She had to be patient.
Her staff rattled against the shield again and again, as she felt her opponent’s defence get weaker and weaker, with the powerful force of her kinetic module focusing the strength of her strikes into a single point. Eventually something would break, his shield of his arm. Once his defences were finally down, she would go in swiftly for the kill.
Her opponent’s frustration won out as his shield shattered and fell to the floor, forcing him to attack Nika with a vicious two handed swipe. She blocked the strike handily, before the Balnath grabbed her staff, locking them in a clinch.
“Giff me sthome help over ‘ere!” The Balnath called out, as Nika reached for a knife, forcing the Balnath to adjust his stance as she stabbed blindly, glancing off armoured plates before finding purchase somewhere, causing her attacker to grunt with pain as he shoved her back, holding her up against a wall.
‘Shit.’ She cursed in her mind. ‘He’s stronger than me, but all I need is a moment to take him by surprise and I can break away and kill him!’
She held strong with her arms, holding the Balnath back as his jaws snapped shut barely an inch away from her neck. He tried again, and she pushed back harder, the jaws snapping shut around nothing, but much closer this time.
He tried again, bringing his vicious maw even closer still…
‘Gotcha!’ Nika thought to herself, as she jerked her head forward in a headbutt, catching the Balnath by surprise and giving the Kizun the space she needed to bring her knees up to her chin, before kicking out as hard as she could into the face of the Balnath, knocking him back with a roar of pain, before he leapt forward with a side swipe that Nika used her tail to quickly dodge, before in the same motion she brought the tip of her staff round and smacked the Balnath as hard as she could, right in the face, the powerful strike shattering its lower jaw completely.
“My fathce!” the attacker got out, clutching what little remained of his lower jaw, before looking up in the next moment as they stared down the barrel of Nika’s shotgun.
“Plea-” They got out, before their head was obliterated in an explosion of dark, blackish blood as their body clattered uselessly to the ground.
“Fuck you.” The Kizun retorted. Using her tail to quickly clip the sword to the magnets of her armour, Nika could see more Regulators in the crowd heading towards the DJ booth. Quickly checking her weapons, she headed right into the brawl!
*****
“You don’t belong here, girlie!” the thug cackled as their cybernetic arm crackled with electric discharge.
“Replacto!” Alora snarled as she swiped her wand out, blasting her attacker with a sudden flash of light that sent him stumbling back, clutching at his eyes.
“Anyone else?” Alora asked, trying her best to channel Nika’s cool, calm demeanour, crossed with Jack’s intimidating presence as the cluster of gangers and mercenaries all looked around at each other for just a moment, before deciding that the Eladrie wasn’t actually that intimidating, as one tried to rush her with a broken chair.
‘Oh by the Mother Tree! How do those two do it?’ Alora cursed in her mind as she summoned her spiritual weapon - a spear of light - that she quickly stabbed at the fish-like Osi, gutting them in the stomach which quickly made them drop the chair, while Alora wisely moved to the side to get out of the vicious melee happening all around her. Where were the others?
‘I have to make sure they’re all right.’ the Eladrie determinedly told herself as she began casting another, more complicated spell…
“Attention all idiots!” The voice over the speakers sneered out over the ever-changing music that the DJ didn’t seem to have any control over. “We discussed this. Though the Outsider is a priority, you target the spellcasters first if you can! Must I do everything myself?”
Thrumming with sudden power, the turrets above them finally opened fire, shooting almost indiscriminately at the crowd below, cutting several of the brawling patrons down before they even knew what hit them.
Chanting and waving her hands around as quickly as she dared, Alora maintained her concentration of her spell, completing it just in time as the turrets finally tracked her as she summoned a great holy aura of light to cover herself that would give her the protection she needed, the Armour of Faith deflecting the lights of the laser turrets harmlessly aside.
A loud bark sounded out, and knowing Dante’s warning for what it was, Alora spun around to see two Regulators, who were both Vulstas fighting through the brawl to get to her. Unlike Rena, these two were males, both carrying plasma shotguns but unable to get effective shots off through the crowd. Not that something like that stopped them from trying…
“Stevarin!” she yelled out, pointing her wand at one of the two who was about to open fire on a downed ganger, as with a flash of yellow light their movements slowed, quickly freezing stiff as a board as they failed to resist the Holding spell, their eyes widening in sheer terror as the gang-mates of their would-be-victim set upon them in a fury with fists and clubs, before a spell cast from the rafters sent all of them clattering to the ground clutching at their minds.
‘One of the enemy mages providing overwatch.’ Alora noted as she quickly looked up for any sign of them, but not seeing them. ‘Under a veil of invisibility no doubt.’
Feeling the dull impact of a shotgun blast dissipate harmlessly against her magical armour, Alora spun round to the other Regulator, cursing her moment of hesitation as the Vulsta drew a long knife with which to get in close with.
Remembering her fight with Izadora all those weeks ago, Alora waved her arms around quickly to summon a bubble of light to engulf her, before quickly following it up with an explosive flash that thundered all around her like a flashbang grenade, while leaving her unharmed.
As the light dissipated, she deftly avoided the blind lunge from the temporarily blinded Regulator, before jamming her spear into his stomach, using her reach advantage to dodge the desperate swipes he sent her way.
“Garrash!” Alora spoke a quick cantrip, using her affinity with life magic to channel poison through the top of her spear. Her already-weakened attacker quickly slumped to the ground as the debilitating effects took hold, but before Alora could pull her spear back, she was hit by a spell that came from above, disrupting her magic and causing her magical spear and armour to disappear.
‘Damn! It’s that mage above me!’ Alora cursed to herself as she quickly ran underneath one of the balconies, as the turrets chased after her with gunfire. ‘You want to hide in the shadows like a coward? I’ve got something to fix that!’
Quickly making sure there weren’t any immediate threats around, Alora quickly rummaged through her pockets for a wand of white crystal she had prepared about a year ago that still had a few charges. Casting quickly, she levelled it towards the ceiling and prayed to all the gods that she was aiming it at where the enemy mage was hiding,
“Glitasha!”
A spray of shining, sparkling particles of light shot out of her wand, puffing out to cover a good half of the ceiling, and as they began to fall to the floor and latch on to the people below, Alora spotted a huddled form by one of the rafters.
‘Got you!’ She thought with satisfaction.
“Ilthax! Get out of there!” The voice over the speakers warned, presumably the name of her target, but it was too late…
“Solaris!” Alora yelled, throwing her palms out in a thrust as a great javelin of light shot out of her palms. The enemy mage had barely moved before it impaled their centre of mass, sending what must have been a fireball spell way off target which blasted apart a huge, gaping hole in the back wall.
The invisible form of the glitterdust-covered mage slowly began to materialise as the blue-furred, ape-like Regulator clutched at their chest in pain, with wide eyes of disbelief at the spear of hard light that had gone right through their torso. As their flight spell dissipated, their lifeless body fell three stories from the rafters to slam down on the ground floor below.
“Nice one Alora!” the Eladrie heard the voice call from behind her as Nika came up next to her, the Kizun bleeding from a cut on her face. “Where are the others?”
“I don’t know. But we need to find them now!” Alora frantically told them as she took in the sheer state of chaos around them. Many broken bodies lay amongst the carnage, and though the Eladrie knew some would likely be still alive at the end of the night, she knew that many would not.
“You don’t need to tell me twice!” Nika agreed with a grim expression.
*****
First/Previous
Looks like Jack, Nika and Alora are holding on for now! But how long can they keep it up?
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https://preview.redd.it/28uxy58q3m0d1.jpg?width=1217&format=pjpg&auto=webp&s=c66a0b61e12cb212d5eca30ed77ef54fcd0470c4
https://imgur.com/a/HKwzj1c

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"A circle centered at point M is tangent to the rectangle ABCD at point K. AB and BL are chords in circle M. Point M is on BL.
A. Prove that angle KML is twice as big as angle KBC.
B. Which of the following statements is true and which is false? Explain.

1. KM is the middle segment in trapezoid DLBC.
2. The area of ΔLMK is equivalent to the area of ΔMKB
3. ΔLAB~ΔBCK

C. Given: BK=a, KL=b. Express the area of BCKM using a and b.
D. Express the ratio of the area of ΔBKL to the area of ΔDKL using a and b."
In B, the true ones are 1 and 2, 3 is incorrect- there's a 90 degree angle, but the other angles on ΔBCK are α and 90-α, and on ΔLAB are 2α and 90-2α (because alternate angles are equal between parallel lines and the sum of acute angles in a right triangle 90 degrees).
I expressed the area of ΔMKB as ab/4 using what I proved on B2, SΔBKL=ab/2, and it's twice as big as MKB. I thought about doing it through SΔMKB+SΔBCK, but I couldn't express the area of ΔBCK, I managed to prove that SΔMKB/SΔBCK is MK/BC, but I couldn't find MK/BC. Next, I proved ΔBKC~ΔBLK, the ratio between the edges got me nowhere. I also used the Pythagoras theorem for ΔBKL, LB²=a²+b², I couldn't do anything with that. Help?

When studying for a math test I have on Thursday (11th grade, practice test for questionnaire 035581), I came across this question and I have no idea how to do C (Translated):
"A circle centered at point M is tangent to the rectangle ABCD at point K. AB and BL are chords in circle M. Point M is on BL.
A. Prove that angle KML is twice as big as angle KBC.
B. Which of the following statements is true and which is false? Explain.

1. KM is the middle segment in trapezoid DLBC.
2. The area of ΔLMK is equivalent to the area of ΔMKB
3. ΔLAB~ΔBCK

C. Given: BK=a, KL=b. Express the area of BCKM using a and b.
D. Express the ratio SΔBKL:SΔDKL using a and b."
In B, the true ones are 1 and 2, 3 is incorrect- there's a 90 degree angle in both, but the other angles on ΔBCK are α and 90-α, and on ΔLAB are 2α and 90-2α (because alternate angles are equal between parallel lines and the sum of acute angles in a right triangle 90 degrees).
I expressed the area of ΔMKB as ab/4 using what I proved on B2, SΔBKL=ab/2, and it's twice as big as MKB. I thought about doing it through SΔMKB+SΔBCK, but I couldn't express the area of ΔBCK, I managed to prove that SΔMKB/SΔBCK is MK/BC, but I couldn't find MK/BC. Next, I proved ΔBKC~ΔBLK, the ratio between the edges got me nowhere. I also used the Pythagoras theorem for ΔBKL, LB²=a²+b², I couldn't do anything with that. Help?

When studying for a math test I have on Thursday (11th grade, practice test for questionnaire 035581), I came across this question and I have no idea how to do C (Translated from Hebrew, the question is in the link):
"A circle centered at point M is tangent to the rectangle ABCD at point K. AB and BL are chords in circle M. Point M is on BL.
A. Prove that angle KML is twice as big as angle KBC.
B. Which of the following statements is true and which is false? Explain.

1. KM is the middle segment in trapezoid DLBC.
2. The area of ΔLMK is equivalent to the area of ΔMKB
3. ΔLAB~ΔBCK

C. Given: BK=a, KL=b. Express the area of BCKM using a and b.
D. Express the ratio of the area of ΔBKL to the area of ΔDKL using a and b."
In B, the true ones are 1 and 2, 3 is incorrect- there's a 90 degree angle, but the other angles on ΔBCK are α and 90-α, and on ΔLAB are 2α and 90-2α (because alternate angles are equal between parallel lines and the sum of acute angles in a right triangle 90 degrees).
I expressed the area of ΔMKB as ab/4 using what I proved on B2, SΔBKL=ab/2, and it's twice as big as MKB. I thought about doing it through SΔMKB+SΔBCK, but I couldn't express the area of ΔBCK, I managed to prove that SΔMKB/SΔBCK is MK/BC, but I couldn't find MK/BC. Next, I proved ΔBKC~ΔBLK, the ratio between the edges got me nowhere. I also used the Pythagoras theorem for ΔBKL, LB²=a²+b², I couldn't do anything with that. Help?

Popped something in my knee tonight when trying to lock up a triangle tighter. I was still square to my partner and I grabbed my ankle to pull up deeper into the back of my knee so I could lock it off and then something went pop in my knee (bent one around their neck). Gave my knee a wack and it went pop again then I could move it again. Now the outside of my knee is sore/burning.
Anyone else done this before? I probably should have cut an angle before locking it off right? I’m concerned this will now be a reoccurring thing. Keen to hear everyone’s thoughts.
Cheers

I'm sketching out a design that looks best from the side, like Phineas, though even Phineas has a few frames where he's cursedly front-facing.
Do you set up your streaming workspace so that your IRL body and head always face off at an angle? Do you rig that front frame and hope it never appears for long in stream? Do you decide to scrap the design and try for one that has better angles all round?
(I'm not actually doing a Disney design, Phineas's triangle was just the most obvious design that came to mind. Or something like Ran's stylized hair horn from Detective Conan that gets weird physics or closeup crops in the anime whenever her head has to rotate.)

Hello math reddit! It has been a very long time since I was in high school and had to do geometry! I am an artist with a hobby for furniture making, and I've come to a bump in the road. A chair I'm designing, I have a quadrilateral (no paralell sides) with all 4 angles and 2 sides known. I need the other two sides. (Top side and bottom side).
In addition, I have a 95° L piece, with 2 sides of 20". If the piece were attached 6" from the top of the quadrilateral, where would the other side intersect? (depth). This is a profile of the chair, I hope it makes sense. The armrest (top side) in orange will be paralell to the seat (blue). I've added a chair similar in shape to what I'm trying to accomplish to help you all visualize.
https://preview.redd.it/jxk3yo91a90d1.png?width=1822&format=png&auto=webp&s=7c068c8de0913dfe48b919185f2fcd812f616532
https://preview.redd.it/q2i5sfgbb90d1.jpg?width=445&format=pjpg&auto=webp&s=edf8c3dbcfaf2d7786a755ce9d19a8e959b33286

Been laying lvp down to change some things in the house, and I'm on the final platform of the staircase. I've been using a heat gun to bend the planks over the nose for the treads instead of buying the separate nose pieces and so far it's looking great. However, I've hit a snag for the last one. The platform is in a triangular shape, but at the end of one side the triangle flattens out to meet the side of the staircase to meet the drywall instead of continuing at the angle. To make matters worse, the nose of the platform stops here and comes straight down to meet the riser. I have no ideas on how to finish this piece and two days of trial and error have burned me out a little bit. Any suggestions would be greatly appreciated, and hopefully I have an accurate enough description for you to picture what I'm trying work with.