Question

use a trigonometric ratio to solve for c. round to two decimal places as necessary. draw (image of a right triangle with one angle 52°, hypotenuse 28, and side c adjacent to the 52° angle)

Explanation:

Step1: Identify adjacent side/hypotenuse

For the $52^\circ$ angle, side $c$ is adjacent, hypotenuse = 28. Use cosine:
$\cos(52^\circ) = \frac{c}{28}$

Step2: Solve for $c$

Rearrange to isolate $c$:
$c = 28 \times \cos(52^\circ)$
Calculate $\cos(52^\circ) \approx 0.6157$, so:
$c \approx 28 \times 0.6157$

Step3: Compute final value

$c \approx 17.24$

Answer:

17.24