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

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, and we want to find the opposite side $b$.

Step2: Substitute values into formula

We know that $\tan30^{\circ}=\frac{b}{25}$. Since $\tan30^{\circ}=\frac{\sqrt{3}}{3}$, we have the equation $\frac{\sqrt{3}}{3}=\frac{b}{25}$.

Step3: Solve for $b$

Cross - multiply to get $b=\frac{25\sqrt{3}}{3}$. Calculate $b=\frac{25\times1.732}{3}\approx14.4$ (rounded to the nearest tenth).

Answer:

14.4 in.