Question

use a trigonometric ratio to solve for a. round to two decimal places as necessary. draw
15
67°
a

Explanation:

Step1: Identify trigonometric ratio

For the $67^\circ$ angle, the side of length 15 is opposite, and $a$ is the hypotenuse. Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(67^\circ) = \frac{15}{a}$

Step2: Rearrange to solve for $a$

Isolate $a$ by cross-multiplying:
$a = \frac{15}{\sin(67^\circ)}$

Step3: Calculate the value

Use $\sin(67^\circ) \approx 0.9205$:
$a \approx \frac{15}{0.9205} \approx 16.29$

Answer:

$16.29$