Another geometry puzzle

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ceptimus
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Another geometry puzzle

Post by ceptimus »

Find the angle ϴ

triangle.png
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Abdul Alhazred
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Re: Another geometry puzzle

Post by Abdul Alhazred »

Aren't the big one and the little one similar triangles?

I'll go with that == 20 degrees.
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ceptimus
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Re: Another geometry puzzle

Post by ceptimus »

Abdul Alhazred wrote: ↑Mon Sep 28, 2020 9:47 pm Aren't the big one and the little one similar triangles?

I'll go with that == 20 degrees.
Spoiler:
I drew it accurately, so you can see that answer is wrong by measuring it on your screen with a protractor. The challenge, though, is to prove the value of theta using geometry or trigonometry.

It can be done with basic high school geometry - no special knowledge needed. But, of course, it's not obvious at first how to tackle it - which is what makes it an interesting puzzle. :)

It can also be done with high school trigonometry - but it can get a bit messy just using sines, cosines and tangents.

There's also probably a reasonably neat way to do it using basic trigonometry and simultaneous equations.
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Witness
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Re: Another geometry puzzle

Post by Witness »

30°.
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Abdul Alhazred
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Re: Another geometry puzzle

Post by Abdul Alhazred »

How did you get there?
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Witness
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Re: Another geometry puzzle

Post by Witness »

Abdul Alhazred wrote: ↑Wed Sep 30, 2020 12:41 pm How did you get there?
https://en.wikipedia.org/wiki/Law_of_sines
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ceptimus
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Re: Another geometry puzzle

Post by ceptimus »

Here's the way I did it, just using basic geometry.
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