Question

practice using trigonometric ratios to solve for missing lengths. which equation could be used to solve for the length of xy? \\(\circ\\) \\(xy = (22)\sin(41^{\circ})\\) \\(\circ\\) \\(xy = (22)\cos(41^{\circ})\\) \\(\circ\\) \\(xy = \frac{22}{\cos(41^{\circ})}\\) \\(\circ\\) \\(xy = \frac{22}{\sin(41^{\circ})}\\)

Explanation:

Step1: Identify sides relative to $\angle Y$

In right $\triangle XYZ$, $\angle Y=41^\circ$, side $XZ=22$ (opposite $\angle Y$), $XY$ is the hypotenuse.

Step2: Choose correct trigonometric ratio

Use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(41^\circ)=\frac{22}{XY}$

Step3: Rearrange to solve for $XY$

Rearrange the formula: $XY=\frac{22}{\sin(41^\circ)}$

Answer:

D. $XY = \frac{22}{\sin(41^\circ)}$