Question

solving for side lengths of right triangles. a right triangle has a 30° angle. the leg adjacent to the 30° angle measures 25 inches. what is the length of the other leg? round to the nearest tenth. 28.9 in. 14.4 in. 43.3 in. 21.7 in.

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 30^{\circ}$ and the adjacent side to the $30^{\circ}$ angle is $a = 25$ inches. Let the other leg (opposite to the $30^{\circ}$ angle) be $x$. So, $\tan30^{\circ}=\frac{x}{25}$.

Step2: Solve for $x$

Since $\tan30^{\circ}=\frac{\sqrt{3}}{3}$, we have $\frac{\sqrt{3}}{3}=\frac{x}{25}$. Cross - multiply to get $x = 25\times\frac{\sqrt{3}}{3}$. Calculate $x=\frac{25\sqrt{3}}{3}\approx\frac{25\times1.732}{3}=\frac{43.3}{3}\approx14.4$ inches.

Answer:

14.4 in