Question

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. ○ 14.4 in. ○ 21.7 in. ○ 28.9 in. ○ 43.3 in.

Explanation:

Step1: Recall trigonometric ratio (tangent)

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 30^\circ$, adjacent leg = 25 in, and the other leg is opposite to $30^\circ$. So $\tan(30^\circ) = \frac{\text{opposite}}{25}$.

Step2: Solve for opposite leg

Rearrange the formula: $\text{opposite} = 25 \times \tan(30^\circ)$. We know $\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.577$. So $\text{opposite} = 25 \times 0.577 \approx 14.4$.

Answer:

14.4 in.