Another geometry puzzle

Stump your fellow simians.
User avatar
ceptimus
Posts: 1361
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

Another geometry puzzle

Post by ceptimus »

Find the angle ϴ

triangle.png
You do not have the required permissions to view the files attached to this post.
User avatar
Abdul Alhazred
Posts: 86933
Joined: Mon Jun 07, 2004 1:33 pm
Title: Yes, that one.
Location: Not quite Chicago

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.
Image "If I turn in a sicko, will I get a reward?"

"Yes! A BIG REWARD!" ====> Click here to turn in a sicko
The arc of the moral universe bends towards chaos.
People who believe God or History are on their side provide the chaos.
User avatar
ceptimus
Posts: 1361
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

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.
User avatar
Witness
Posts: 31022
Joined: Thu Sep 19, 2013 5:50 pm

Re: Another geometry puzzle

Post by Witness »

30°.
User avatar
Abdul Alhazred
Posts: 86933
Joined: Mon Jun 07, 2004 1:33 pm
Title: Yes, that one.
Location: Not quite Chicago

Re: Another geometry puzzle

Post by Abdul Alhazred »

How did you get there?
Image "If I turn in a sicko, will I get a reward?"

"Yes! A BIG REWARD!" ====> Click here to turn in a sicko
The arc of the moral universe bends towards chaos.
People who believe God or History are on their side provide the chaos.
User avatar
Witness
Posts: 31022
Joined: Thu Sep 19, 2013 5:50 pm

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
User avatar
ceptimus
Posts: 1361
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

Re: Another geometry puzzle

Post by ceptimus »