Question

find the missing side.
round to the nearest tenth.
remember: sohcahtoa

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side (\(25\)) to the angle \(37^{\circ}\) and we need to find the hypotenuse (\(z\)). Using the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), where \(\theta = 37^{\circ}\), adjacent \(= 25\), and hypotenuse \(=z\). So, \(\cos(37^{\circ})=\frac{25}{z}\).

Step2: Solve for \(z\)

Rearrange the formula to \(z=\frac{25}{\cos(37^{\circ})}\). We know that \(\cos(37^{\circ})\approx0.7986\). Then \(z=\frac{25}{0.7986}\approx31.3\).

Answer:

\(31.3\)