Question

a right triangle has a $30^\circ$ angle. the leg adjacent to the $30^\circ$ angle measures 25 inches. what is the length of the other leg? round to the nearest tenth.\
\bigcirc 14.4 in.\
\bigcirc 21.7 in.\
\bigcirc 28.9 in.\
\bigcirc 43.3 in.

Explanation:

Step1: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite leg}}{\text{adjacent leg}}$. Here, $\theta = 30^\circ$, adjacent leg = 25 inches, and we solve for the opposite leg (the other leg).

Step2: Rearrange to solve for opposite leg

$\text{Opposite leg} = \text{Adjacent leg} \times \tan(30^\circ)$
Substitute values: $\text{Opposite leg} = 25 \times \tan(30^\circ)$
Since $\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.5774$, calculate:
$\text{Opposite leg} \approx 25 \times 0.5774$

Step3: Compute final value

$\text{Opposite leg} \approx 14.435$
Round to nearest tenth: $\approx 14.4$

Answer:

14.4 in.