Question

find the missing side.
19
36°
y
(right angle symbol)
y = ?

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with hypotenuse 19, angle \(36^\circ\), and adjacent side \(y\) to the angle. The cosine function relates the adjacent side and the hypotenuse: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Substitute the values

Substitute \(\theta = 36^\circ\), hypotenuse \(= 19\), and adjacent \(= y\) into the cosine formula: \(\cos(36^\circ)=\frac{y}{19}\).

Step3: Solve for \(y\)

Multiply both sides by 19: \(y = 19\times\cos(36^\circ)\). Calculate \(\cos(36^\circ)\approx0.8090\), so \(y\approx19\times0.8090\approx15.37\).

Answer:

\(y\approx15.37\) (or more precise value depending on calculator precision, e.g., using calculator for \(\cos(36^\circ)\) gives \(y\approx19\times\cos(36^\circ)\approx15.37\))