Question

find y.

write your answer in simplest radical form.

feet

Explanation:

Step1: Identify adjacent side to 60°

The side adjacent to the 60° angle is 19 ft, and $y$ is the hypotenuse. Use cosine:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(60^\circ) = \frac{19}{y}$
We know $\cos(60^\circ) = \frac{1}{2}$, so:
$\frac{1}{2} = \frac{19}{y}$

Step3: Solve for y

Cross-multiply to isolate $y$:
$y = 19 \times 2$

Answer:

38 feet