A30°-60°-90° triangle has a hypotenuse with a length of 10. what is the length of the longer leg of the triangle?

a.
5

b.

5 square root of 3

c.

5 square root of 2

d.
20

A 30°-60°-90° triangle is an example of a "special right triangle". The leg opposite the 30° angle will be one times a variable in length. The leg opposite the 60° angle will be the variable multiplied by the root of 3 in length. The hypotenuse will be 2 times the variable. Since the hypotenuse is 10, which is two times the variable, the variable will be 5. We are looking for the longer leg, which is opposite the 60° angle. So that means the length of the longer leg will be 5 roots of 3.

The first one is correct