I have the angles and height of an isosceles triangle. How do I find the side lengths?

Question

This is for a 15-year-old geometry student.

Answer 1

If you have the angles and height, you have it in the bag already. Per definitions of trig functions, for a right triangle (comprising as segments: the side, the height, and 1/2 the base): sin(angle) = opposite/hypotenuse = height/adjacent_side. So take the sine of your angle, and equate it to the height/adjacent_side. Can you solve this single equation in one unknown?