Question

use a trigonometric ratio to solve for d. round to two decimal places as necessary. draw (image of a right triangle with angle 33 degrees at the top, side d as the hypotenuse, and the horizontal leg as 19)

Explanation:

Step1: Identify trigonometric ratio

For the $33^\circ$ angle, the side of length 19 is opposite, and $d$ is the hypotenuse. Use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(33^\circ)=\frac{19}{d}$

Step2: Rearrange to solve for $d$

Isolate $d$ by cross-multiplying:
$d=\frac{19}{\sin(33^\circ)}$

Step3: Calculate the value

Use $\sin(33^\circ)\approx0.5446$:
$d\approx\frac{19}{0.5446}\approx34.89$

Answer:

$34.89$