Question

use a trigonometric ratio to solve for z. round to two decimal places as necessary.
draw
(right triangle with hypotenuse 25, angle 66° at the bottom right, and base z)

Explanation:

Step1: Identify adjacent-hypotenuse ratio

We use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
Here, $\theta=66^\circ$, adjacent side $=z$, hypotenuse $=25$.

Step2: Rearrange to solve for z

$z = 25 \times \cos(66^\circ)$

Step3: Calculate the value

$\cos(66^\circ) \approx 0.4067$, so $z \approx 25 \times 0.4067$

Answer:

$10.17$