a right triangle has a 30° angle. the leg adjacent to the 30° angle measures 25 inches. what is the length…

Answer:

D. 43.3 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 25 inches. Let the length of the other leg (opposite to the $30^{\circ}$ angle) be $x$. So $\tan30^{\circ}=\frac{x}{25}$.

Step2: Substitute the value of tangent

We know that $\tan30^{\circ}=\frac{\sqrt{3}}{3}$. Then $\frac{\sqrt{3}}{3}=\frac{x}{25}$.

Step3: Solve for $x$

Cross - multiply to get $x = 25\times\tan30^{\circ}=25\times\frac{\sqrt{3}}{3}\approx25\times0.577 = 14.425$ (this is wrong. We want the leg opposite the $60^{\circ}$ angle). Let's start over. If the adjacent side to the $30^{\circ}$ angle is 25 inches, and we want the side opposite the $60^{\circ}$ angle. Using $\tan60^{\circ}=\sqrt{3}=\frac{x}{25}$. Cross - multiply: $x = 25\sqrt{3}\approx25\times1.732=43.3$ inches.