Question

use a trigonometric ratio to solve for c. round to two decimal places as necessary. draw c 65° 16

Explanation:

Step1: Identify the trigonometric ratio

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 65^{\circ}$, the opposite - side to the angle $\theta$ is 16 and the hypotenuse is $c$. So, $\sin65^{\circ}=\frac{16}{c}$.

Step2: Solve for $c$

We can re - arrange the equation $\sin65^{\circ}=\frac{16}{c}$ to get $c=\frac{16}{\sin65^{\circ}}$. Since $\sin65^{\circ}\approx0.9063$, then $c=\frac{16}{0.9063}\approx17.65$.

Answer:

$17.65$