Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side to the angle $29^{\circ}$ is 20 and we want to find the hypotenuse $z$. We use the cosine ratio $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(29^{\circ})=\frac{20}{z}$.

Step2: Solve for $z$

Cross - multiply to get $z\times\cos(29^{\circ}) = 20$. Then $z=\frac{20}{\cos(29^{\circ})}$.

Step3: Calculate the value

We know that $\cos(29^{\circ})\approx0.8746$. So, $z=\frac{20}{0.8746}\approx22.87$.

Answer:

$22.87$