# Triangle question

• Apr 2nd 2010, 12:18 AM
billionj
Triangle question
I have a need to determine the length of the third side of an isosceles triangle. The angles are 36, 72, 72, and the long sides are 1100 feet. What is the formula for the third side please? I'm not a trig guy so if you could give me the answer AND the formula that would be great (just in case I can't understand the formula).

Thank you very much.
• Apr 2nd 2010, 12:37 AM
Hello billionj

Welcome to Math Help Forum!
Quote:

Originally Posted by billionj
I have a need to determine the length of the third side of an isosceles triangle. The angles are 36, 72, 72, and the long sides are 1100 feet. What is the formula for the third side please? I'm not a trig guy so if you could give me the answer AND the formula that would be great (just in case I can't understand the formula).

Thank you very much.

Imagine that you cut the isosceles triangle straight down the middle from vertex to base, to form two identical right-angled triangles. Then in one of these triangles, the hypotenuse is $\displaystyle 1100$ feet long, and the angle adjacent to the base is $\displaystyle 72^o$. So the length of the base is:
$\displaystyle 1100\cos 72^o$
This is just one-half of the base of the original triangle. So its length is:
$\displaystyle 2\times1100\cos 72^o = 680$ feet (to the nearest foot)