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: $\tan(\theta) = \frac{\text{opposite leg}}{\text{adjacent leg}}$, where $\theta=30^\circ$, adjacent leg $=25$ in, opposite leg is the unknown leg $x$.

Step2: Rearrange to solve for $x$

$x = 25 \times \tan(30^\circ)$

Step3: Calculate the value

$\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.5774$, so $x \approx 25 \times 0.5774 = 14.435$

Step4: Round to nearest tenth

$x \approx 14.4$

Answer:

14.4 in.