Question

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

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the hypotenuse (17) and we need to find the opposite side to the \(13^\circ\) angle (which is \(c\)). The sine ratio is \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(13^\circ)=\frac{c}{17}\).

Step2: Solve for \(c\)

Multiply both sides by 17: \(c = 17\times\sin(13^\circ)\). Calculate \(\sin(13^\circ)\approx0.2250\). Then \(c\approx17\times0.2250 = 3.825\), round to two decimal places.

Answer:

\(3.83\)