Question

find the missing side.
19
36° y
y = ?
round to the nearest tenth.
remember: sohcahtoa

Explanation:

Step1: Identify the trigonometric ratio

We know the hypotenuse (\(19\)) and need to find the adjacent side (\(y\)) to the angle \(36^{\circ}\). Using the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos(36^{\circ})=\frac{y}{19}\).

Step2: Solve for \(y\)

Multiply both sides by \(19\): \(y = 19\times\cos(36^{\circ})\). Using a calculator, \(\cos(36^{\circ})\approx0.809\), then \(y\approx19\times0.809 = 15.4\).

Answer:

\(15.4\)