Question

If the triangle is a 60-90-30 triangle and has a hypothenuse of 16, how would I solve for the missing two sides?

Answer 1

shorter leg = 8

longer leg = 8√3

Explanation:

If the hypotenuse of the 60-90-30 triangle is 16, we can use the ratios of the sides to find the lengths of the other two sides. Here's how we can solve for the missing sides:

The length of the shorter leg (opposite the 60-degree angle) is half the length of the hypotenuse:

shorter leg = (1/2) * hypotenuse

= (1/2) * 16

= 8

The length of the longer leg (opposite the 30-degree angle) can be found using the ratio of the sides in a 30-60-90 triangle:

longer leg = shorter leg · √3

= 8√3

So, the missing side of the triangle are 8 and 8√3