Question

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

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 32^{\circ}$, the adjacent side to the $32^{\circ}$ angle is 28, and the hypotenuse is $b$. So, $\cos32^{\circ}=\frac{28}{b}$.

Step2: Solve for $b$

We can rewrite the equation as $b=\frac{28}{\cos32^{\circ}}$. Since $\cos32^{\circ}\approx0.8480$, then $b=\frac{28}{0.8480}\approx33.02$.

Answer:

$33.02$