Question

find the measure of side a.
(1 point)
options: 12, 14, 5, 10

Explanation:

Step1: Identify trigonometric ratio

In right $\triangle ABC$, side $a$ is opposite $\angle A$, and $c$ is the hypotenuse. Use sine function:
$\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}$

Step2: Substitute known values

$\sin(41^\circ) = \frac{a}{16}$
Rearrange to solve for $a$:
$a = 16 \times \sin(41^\circ)$

Step3: Calculate the value

$\sin(41^\circ) \approx 0.6561$, so:
$a \approx 16 \times 0.6561 = 10.4976$

Answer:

10