Question

use a trigonometric ratio to solve for b. round to two decimal places as necessary.
show your work here
b =

Explanation:

Step1: Identify the trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 41^{\circ}$, the opposite side to $\theta$ is $21$ and the adjacent side is $b$. So $\tan41^{\circ}=\frac{21}{b}$.

Step2: Solve for $b$

Cross - multiply to get $b\times\tan41^{\circ}=21$. Then $b = \frac{21}{\tan41^{\circ}}$.

Step3: Calculate the value

We know that $\tan41^{\circ}\approx0.8693$. So $b=\frac{21}{0.8693}\approx24.16$.

Answer:

$24.16$