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The value of x (sh.itjust.works)
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[-] Habahnow@sh.itjust.works 64 points 1 month ago

All these people saying its 135 are making big assumptions that I think is incorrect. There’s one triangle (the left one) that has the angles 40, 60, 80. The 80 degrees is calculated based on the other angles. What's very important is the fact that these triangles appear to have a shared 90 degree corner, but that is not the case based on what we just calculated. This means the image is not to scale and we must not make any visual assumptions. So that means we can’t figure out the angles of the right triangle since we only have information of 1 angle (the other can’t be figured out since we can’t assume its actually aligned at the bottom since the graph is now obviously not to scale).

Someone correct me if I'm wrong.

[-] Brosplosion@lemm.ee 56 points 1 month ago

135 is correct. Bottom intersection is 80/100, 180-35-100 = 45 for the top of the second triangle. 180 - 45 = 135

[-] Leate_Wonceslace@lemmy.dbzer0.com 26 points 1 month ago

Mathematician here; I second this as a valid answer. (It's what I got as well.)

[-] PresidentCamacho@lemm.ee 14 points 1 month ago

Random guy who didn't sleep in middle school here: I also got the same answer.

[-] myusernameis@lemmy.ca 7 points 1 month ago

Random woman who didn't sleep very well last night. I got a different answer, then thought about it for 10 more seconds and then got 135.

(No I didn't assume the right angle, my mistake was even dumber. I need a nap.)

[-] TheOakTree@lemm.ee 14 points 1 month ago

You're making the assumption that the straight line consisting of the bottom edge of both triangles is made of supplementary angles. This is not defined due to the nature of the image not being to scale.

[-] NoMoreLurkingToo@startrek.website 22 points 1 month ago

Unless there are lines that are not straight in the image (which would make the calculation of x literally impossible), the third angle of the triangle in the left has to be 80°, making the angle to its right to be 100°, making the angle above it to be 45°, making the angle above it to be 135°. This is basic trigonometry.

[-] Windex007@lemmy.world 0 points 1 month ago

which would make the calculation of x literally impossible

Yes.

But that doesn't mean that line must be straight. It just means if it isn't, you can't derive x.

[-] Siethron@lemmy.world 1 points 1 month ago

When you're finding the outside angle along the line of a triangle you don't need the inside angle tied to that outside angle if you have the other two inside angles since both straight lines and triangles total to 180 degrees.

[-] brisk@aussie.zone 39 points 1 month ago

This is a standard way to draw geometric proofs, it's not at all unreasonable to assume straight lines alongside unrepresentative angles. It's certainly still an assumption, but a conventional one.

[-] qarbone@lemmy.world 21 points 1 month ago

I mean, the assumption shouldn't be anything about scale. It should be that we're looking at straight lines. And if we can't assume that, then what are we even doing.

But, assuming straight lines, given straight lines you find the other side of an intersecting line because of complements.

[-] ComicalMayhem@lemmy.world 4 points 1 month ago

And if we can't assume that, then what are we even doing

That's exactly what the other user is saying. We can't assume straight lines because the given angles don't make any sense and thus this graph is literally impossible to make. We're arguing over literal click bait is what we're doing.

[-] qarbone@lemmy.world 16 points 1 month ago

Why do the labeled angles prevent us from assuming straight lines?

[-] starman2112@sh.itjust.works 2 points 1 month ago

Because the angles aren't represented accurately. It could be that the two angles that look like they're 90° add up to 180°, but they could also not

[-] sugar_in_your_tea@sh.itjust.works 3 points 1 month ago

That's technically possible, but that's also an irrational take. The rational take is to assume the problem is solvable given the available information, which means assuming that the lines are straight.

Yes, two angles appear to be 90⁰, but they're obviously not with the given information. Math conventions nearly always label right angles, so not having the right angle there implies that the angle should not be assumed to be 90⁰. Math conventions in trigonometry also generally assume straight lines unless there's a visual indicator that they're not, and those tend to be exaggerated so it's obvious.

So the rational answer here is that the bottom line is straight and therefore the problem is solvable. Saying otherwise is irrational, because that's so far away from math conventions.

[-] ochi_chernye@startrek.website -4 points 1 month ago

Because the apparently straight lines contradict the labels. As drawn, the unlabeled bottom vertices are clearly 90°, not 80° and 100°. We must either conclude that the labels are incorrect, or that the figure is not drawn to scale. Either way, it's insoluble.

[-] TheOakTree@lemm.ee 2 points 1 month ago* (last edited 1 month ago)

We can't assume that the straight line across the bottom is a straight line because the angles in the drawing are not to scale. Who's to say that the "right angle" of the right side triangle isn't 144°?

If the scale is not consistent with euclidian planar geometry, one could argue that the scale is consistent within itself, thus the right triangle's "right angle" might also be 80°, which is not a supplement to the known 80° angle.

[-] MeThisGuy@feddit.nl 1 points 1 month ago

thx for the compliment

[-] bstix@feddit.dk 7 points 1 month ago

I'd argue that the bottom line is indeed one continuous line regardless of how many other lines intersect on it, because there's nothing indicating that the line is broken at the intersection.

Now the only reason I think the lines are straight at all is use of the angular notations at the ends, which would be horribly misleading to put at the end of curves or broken lines.

[-] Maggoty@lemmy.world 7 points 1 month ago

Stupid stuff like this is why kids hate math class. Unless the problem says calculate all unmarked angles, those visually 90 degree angles are 90 degrees. It works that way in any non engineering job that uses angles because it's common sense.

[-] TheOakTree@lemm.ee 14 points 1 month ago* (last edited 1 month ago)

...what? I get that this drawing is very dysfunctional, but are you going to argue that a triangle within a plane can have a sum of angles of 190°?

[-] Maggoty@lemmy.world 15 points 1 month ago

Nope I'm not saying that. I'm saying this is a gotcha question that demotivates learners.

[-] TheOakTree@lemm.ee 8 points 1 month ago

I see. I agree completely. The only place this belongs is as a thought experiment on making assumptions in geometry.

[-] NoMoreLurkingToo@startrek.website 2 points 1 month ago

The sum of the angles of a triangle are always 180°

[-] TheOakTree@lemm.ee 4 points 1 month ago

Yes, I believe I implied this by suggesting that the sum of angles being 190° is absurd.

[-] starman2112@sh.itjust.works 0 points 1 month ago

No, they're saying that unless you're already good at this stuff, it's easy to assume that a visually 90° angle is actually 90° even when it's not

[-] taladar@sh.itjust.works 1 points 1 month ago

Especially if you are bad at this stuff you know that drawing anything like that accurately is a real pain and nobody who can avoid it will ever do it to represent anything accurately. That is what labels are for.

[-] wanderer@lemmy.world 3 points 1 month ago

You're making the assumption that they are triangles.

[-] the_wise_wolf@feddit.org 0 points 1 month ago

Your assumption is that it's a Cartesian coordinate system with 90° angles. But that's not necessarily the case. You can apply a sheer transformation to correct for the unusual appearance. When you do that, the angles change, but straight lines stay straight and parallels stay parallel. There's a mathematical term for that, which I can't remember right now.

this post was submitted on 08 Oct 2024
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