Question

The length of the hypotenuse in a 30°-60°-90° triangle is 6√10yd. What is thelength of the long leg?

Answer 1

In order to calculate the length of the long leg, we can use the sine relation of the 60° angle.

The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.

So we have:

`\begin{gathered} \sin (60\degree)=\frac{x}{6\sqrt[]{10}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{6\sqrt[]{10}} \\ 2x=6\sqrt[]{30} \\ x=3\sqrt[]{30} \end{gathered}`

So the length of the long leg is 3√30 yd.