Question

use a trigonometric ratio to solve for a. round to two decimal places as necessary.
draw
right triangle with right angle at top left, horizontal leg length 20, vertical leg labeled a, angle at bottom left 64°

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the opposite side to the \(64^\circ\) angle as \(20\) and the adjacent side as \(a\). The tangent ratio is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan(64^\circ)=\frac{20}{a}\).

Step2: Solve for \(a\)

Rearrange the formula: \(a = \frac{20}{\tan(64^\circ)}\). Calculate \(\tan(64^\circ)\approx2.0503\), then \(a=\frac{20}{2.0503}\approx9.75\).

Answer:

\(9.75\)