Question

determine the value of a. round your answer to the nearest tenth.
right triangle with right angle at the bottom right, hypotenuse 18, angle at the top 36 degrees, horizontal leg a, vertical leg b

Explanation:

Step1: Identify trigonometric ratio

For the $36^\circ$ angle, side $a$ is opposite, hypotenuse is 18. Use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(36^\circ)=\frac{a}{18}$

Step2: Solve for $a$

Rearrange to isolate $a$: $a = 18\times\sin(36^\circ)$
Calculate $\sin(36^\circ)\approx0.5878$, so $a\approx18\times0.5878$

Step3: Compute and round

$a\approx10.5804$, round to nearest tenth: $a\approx10.6$

Answer:

10.6