If you know the height of a triangle what formula will give you the lengths of the other 2 sides?

Question

What formula do you use to find lengths of a right triangle if you only know the height and angle of one of the sides opposite the 90 degree side?

Answer 1

If you are given one of the angles in a right triangle, you know the other. All the angles in any triangle add up to 180 degrees. A right triangle is so named because one angle is 90 degrees. That leaves 90 degrees for the other two angles. Subtract the known angle from 90 and you have the third angle.

You can use any angle and the side opposite that angle to determine the length of the hypotenuse (c). Knowing angle A and the length of side a:

sin A = a / c    c * sin A = a    c = a / (sin A)

You now know the length of the hypotenuse, and you have calculated the size of angle B (note above). You can determine the length of side b:

c * sin B = b