Question

use a trigonometric ratio to solve for d. round to two decimal places as necessary.
draw
(right triangle with one leg 25, angle 51° at the top, and side d as the other leg)

Explanation:

Step1: Identify trigonometric ratio

For the $51^\circ$ angle, the side of length 25 is opposite, and $d$ is adjacent. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(51^\circ) = \frac{25}{d}$

Step3: Rearrange to solve for $d$

$d = \frac{25}{\tan(51^\circ)}$

Step4: Calculate the value

Use $\tan(51^\circ) \approx 1.2349$, so:
$d \approx \frac{25}{1.2349} \approx 20.24$

Answer:

$20.24$