Question

use a trigonometric ratio to solve for x. round to two decimal places as necessary. draw right triangle with angle 52°, hypotenuse 15, and x as the adjacent side to 52°

Explanation:

Step1: Identify adjacent side/hypotenuse

For the $52^\circ$ angle, $x$ is the adjacent side, and the hypotenuse is 15. Use cosine ratio:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(52^\circ) = \frac{x}{15}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = 15 \times \cos(52^\circ)$
Calculate $\cos(52^\circ) \approx 0.6157$, so:
$x \approx 15 \times 0.6157$

Step4: Compute final value

$x \approx 9.2355$

Answer:

$x \approx 9.24$