# Thread: Looking easy but hard question on geometry

1. ## You are right. Thank you.

Originally Posted by Dr.Peterson
It IS an isosceles triangle: both base angles are 80 degrees.

But it's great that your group worked it out. It's a big challenge.
I'll try to do it without the circle. I thought it over and recalled that we needed the circle to solve it.

2. Originally Posted by yma16
I'll try to do it without the circle. I thought it over and recalled that we needed the circle to solve it.
I think the circle was a wonderful idea; I wasn't saying there's any reason to try for another proof.

But this problem is the type where people can enjoy the challenge of finding as many different proofs as they can, so have fun with it if you wish.

3. ## another solution using law of sine

ScreenHunter_33 Feb. 24 08.18.jpg
Originally Posted by Dr.Peterson
I think the circle was a wonderful idea; I wasn't saying there's any reason to try for another proof.

But this problem is the type where people can enjoy the challenge of finding as many different proofs as they can, so have fun with it if you wish.

4. Interesting. I think the last expression was copied wrong, but the result is correct. I'd be happier with a method that gave an exact value (not one that you get as a decimal approximation); it might be fun to try to show that it is exactly 20.

5. ## I change the last expression. Here is deduction of x

IMG_0131.jpg

in the 3rd expression from the bottom the + should be - in front of 4sin

6. You're my kind of person! You took the challenge.

I'm sure that work can be shortened a bit, but it's definitely a proof.