Question

use a trigonometric ratio to solve for y. round to two decimal places as necessary. draw (right triangle with horizontal leg 21, vertical leg y, and the angle at the bottom vertex is 49°) show your work here

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with angle \(49^\circ\), opposite side to the angle is \(21\) and adjacent side is \(y\). So we use \(\tan\) ratio: \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(49^\circ)=\frac{21}{y}\)

Step2: Solve for \(y\)

Rearrange the formula: \(y = \frac{21}{\tan(49^\circ)}\)
Calculate \(\tan(49^\circ)\approx1.1504\)
Then \(y=\frac{21}{1.1504}\approx18.25\)

Answer:

\(18.25\)