Question

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

Explanation:

Step1: Identify sides relative to $\angle Y$

• $\angle Y = 41^\circ$, side $XZ = 22$ (opposite $\angle Y$), $XY$ = hypotenuse, $YZ$ = adjacent to $\angle Y$.

Step2: Select correct trigonometric ratio

Use sine (opposite/hypotenuse):
$\sin(41^\circ) = \frac{XZ}{XY}$

Step3: Rearrange to solve for $XY$

Substitute $XZ=22$, rearrange:
$XY = \frac{22}{\sin(41^\circ)}$

Answer:

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