Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In the right - triangle, the angle $\theta = 32^{\circ}$, the opposite side to the $32^{\circ}$ angle is 23 and the hypotenuse is $a$. So, $\sin32^{\circ}=\frac{23}{a}$.

Step2: Solve for $a$

We can rewrite the equation $\sin32^{\circ}=\frac{23}{a}$ as $a=\frac{23}{\sin32^{\circ}}$. Since $\sin32^{\circ}\approx0.5299$, then $a=\frac{23}{0.5299}\approx43.40$.

Answer:

$43.40$