Question

use a trigonometric ratio to solve for a. round to two decimal places if necessary. draw

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the angle $12^\circ$, the opposite side to this angle is 21, and $a$ is the hypotenuse. We use the sine ratio: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(12^\circ)=\frac{21}{a}$

Step3: Rearrange to solve for $a$

$a=\frac{21}{\sin(12^\circ)}$

Step4: Calculate the value

First, $\sin(12^\circ)\approx0.2079$, so $a\approx\frac{21}{0.2079}\approx101.01$

Answer:

$101.01$