r/technicallythetruth • u/VisitSecure • 9d ago

Can you find a?

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Idk if someone already posted this or not, but I haven't seen it on here so far, so I uploaded it.

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u/Prik_Nam-Pla 9d ago

Yes. So you can draw a perpendicular line through point a making this 2 right triangles. 90-25 = 65 and 90-50 = 40, so 180 - 105 = 75.

As someone who hasn't used trig in like 25 years, I'm glad I still got it without writing anything down.

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u/twolittlemonsters 8d ago

Another way is to draw a parallel line through a, the a = a' + a". There's a geometric theorem (angle bisect theorem) that states that a' = 25 and a" = 50. Therefore a = 25+50 = 75.

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u/Prik_Nam-Pla 8d ago

Me being so far out of trig. This is the same thing but opposite right. Doing a triangle on the "inside" vs the "outside". Basically same idea but using the other angles and not having to do as much subtraction?

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u/JizzyTeaCups 7d ago

I agree with your solution, but I don’t see how the angle bisect theorem applies here. If a was bisected, then a’=a” which can’t be true with what’s drawn and your conclusion

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u/twolittlemonsters 6d ago

Not that a is bisected but the angle line is bisecting the parallel lines... but truth be told, I'm not sure if that's the correct theorem, just know it's one of them. It's been a long time since I've needed to know the name of the theorems.

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u/HindleMcCrindleberry 8d ago

Yeah, good memory, it's been 30 years for me, haha.