Question

use a trigonometric ratio to solve for z. round to two decimal places as necessary.
draw
show your work here

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the hypotenuse (16) and we need to find the opposite side to the 37° angle (z). The sine ratio is \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin(37^\circ)=\frac{z}{16}\)

Step2: Solve for z

Multiply both sides by 16: \(z = 16\times\sin(37^\circ)\)
Using a calculator, \(\sin(37^\circ)\approx0.6018\)
Then \(z\approx16\times0.6018 = 9.6288\approx9.63\)

Answer:

\(z\approx9.63\)