Question

Find n (write in simplest radical form)

Answer 1

This is a special right triangle called a 30-60-90 triangle. It has a special property the relates the ratio of side lengths. That ratio is 1:$\sqrt{3}$:2

What does this mean? If you know the shortest side of a 30-60-90 triangle, you can find the longer leg by multiplying it by $\sqrt{3}$, and you can find the hypotenuse by multiplying the short leg by 2.

In the picture, note that the short leg of the triangle has a length of 9. Therefore, the long leg(or n) is simply 9$\sqrt{3}$