Geometry Question

[Dandy]

Okay, it's been a long time since I used what I learned in geometry unless it was shooting pool or something like that. I am installing in-ceiling speakers, and the location of my front speakers can be pinpointed by geometry if I am thinking correctly. It would be easy if I knew what a 26 degree angle looked like in my head and I could be exactly on target on each side, but alas I can not. I know that I could do it with a protractor, a chalkline, and some measuring tape, but it seems like learning how to figure this out in my head will come in handy for the future.

 

Two sides of the triangle are 15 feet, and the angle of those two sides is 26 degrees. What is the length of the third side? When answering, please remind me of the formula used to reach the answer. I know the pythagorean theorem is a^2 + b^2 = c ^2, but that is for right triangles. Thanks for any help you can give me!

[Mike wanna be]

Just the answer: Third side's just shy of 6.75 feet long.

 

How you get it: You've got an isosceles triangle, so you need to bisect the 26 degree angle and make two right triangles; you know the hypotenuse (15 feet), you know an angle (13 degrees, half of the 26 between the 15-foot sides), so you get:

(sin 13) * 15 = x

x ~ 3.375

But since you bisected the angle, you also bisected the third side of your original triangle, so you need to double that to get the whole thing.

2x ~ 6.75

[Dandy]

Thanks for the answer, and double thanks for the formula (which I had forgotten YEARS ago)!

[Guest Desensitized]

[Slayer]

Easier than splitting the triangle would be using the Law of Cosines, which is the general case of the Pythagorean Theorem as applied to all triangles, not just right ones

[Guest Desensitized]

You really pulled that out of your magic bag of trigs.

[Guest Tzar Lysergic]

Again, fucking choke yourself.

[Guest Desensitized]

Even I knew that one was bad. We need to establish an official TSM Bad Pun Leaderboard Sponsored By Vitamin Water or something.

[Guest Tzar Lysergic]

That's two for you. Edwin and I each had one.