Question

The longer leg of a 30°-60°-90° triangle measures 9 inches What is the length of the shorter leg? OA. 6 inches OB. 3/2 inches OC. 673 inches OD. 313 inches Reset Next Question

Answer 1

As we can see in the graph, the shorter leg is the side opposite the angle 30°, therefore we are going to find it with function tan(x)

`\begin{gathered} \tan (x)=\frac{\text{Opposite Side (shorter leg)}}{\text{Adjacent Side(longer leg)}}=\frac{x}{9\text{ in}} \\ \tan (30)=(x)/(9) \\ \frac{\sqrt[]{3}}{3}=(x)/(9)\text{ ,Since }\tan (30)=\frac{\sqrt[]{3}}{3}\text{ } \\ \frac{\sqrt[]{3}}{3}\cdot9=x\text{ ,Isolating x} \\ 3\sqrt[]{3}=x\text{ ,Simplifying} \\ \text{Shorter side length is x=}3\sqrt[]{3}\text{ } \end{gathered}`

Answer is option D.