Question

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

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the opposite side to the \(50^\circ\) angle as \(22\) and the adjacent side as \(b\). The tangent ratio is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan(50^\circ)=\frac{22}{b}\).

Step2: Solve for \(b\)

Rearrange the formula: \(b = \frac{22}{\tan(50^\circ)}\). Calculate \(\tan(50^\circ)\approx1.1918\), then \(b=\frac{22}{1.1918}\approx18.46\).

Answer:

\(18.46\)