Question

The shorter leg of a 30°-60°-90° triangle measures 9sqrt3 inches. What is the length of the longer leg? OA. 27 inches OB. 27sqrt3 inches OC. 18 inches OD. 18sqrt3 inches

Answer 1

We know that the proportion of the sides of a 30°-60°-90° triangle is:

The shorter leg is K, then:

`K=9\sqrt[]{3}\text{ in}`

Using this result, we can calculate the length of the longer leg:

`\begin{gathered} \sqrt[]{3}K=\sqrt[]{3}\cdot9\cdot\sqrt[]{3}=9\cdot3 \\ \Rightarrow=27\text{ in} \end{gathered}`