Question

find the measure of side a.
(there is a right triangle in the picture, with right angle at c. angle at a is 36 degrees. the hypotenuse ab is labeled c = 12 m. side bc is labeled a, and side ac is the other leg. then below: a = \square m (round the answer to the nearest whole number.))

Explanation:

Step1: Identify trigonometric ratio

For angle $A=36^\circ$, side $a$ is opposite, hypotenuse $c=12$. Use sine:
$\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}$

Step2: Rearrange to solve for $a$

$a = c \times \sin(A)$
Substitute values:
$a = 12 \times \sin(36^\circ)$

Step3: Calculate and round

$\sin(36^\circ) \approx 0.5878$, so:
$a \approx 12 \times 0.5878 = 7.0536$
Round to nearest whole number.

Answer:

7 m