Question

use a trigonometric ratio to solve for b. round to two decimal places as necessary.
draw
(right triangle with one angle 51°, hypotenuse 22, side b adjacent to 51°)

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, the cosine of an angle is defined as the adjacent side over the hypotenuse. Here, angle is \(51^\circ\), adjacent side is \(b\), hypotenuse is \(22\). So \(\cos(51^\circ)=\frac{b}{22}\).

Step2: Solve for \(b\)

Multiply both sides by \(22\): \(b = 22\times\cos(51^\circ)\). Calculate \(\cos(51^\circ)\approx0.6293\), then \(b\approx22\times0.6293 = 13.8446\approx13.84\).

Answer:

\(13.84\)