Question

which equation could be used to solve for the length of xy?
○ xy = (22)sin(41°)
○ xy = (22)cos(41°)
○ xy = \frac{22}{cos(41°)}
○ xy = \frac{22}{sin(41°)}

Explanation:

Step1: Recall sine - cosine definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $XYZ$ with right - angle at $Z$, if the angle $\angle Y = 41^{\circ}$ and the side $YZ = 22$, and we want to find the hypotenuse $XY$.

Step2: Apply cosine formula

We know that $\cos\angle Y=\frac{YZ}{XY}$. Given $\angle Y = 41^{\circ}$ and $YZ = 22$, we can rewrite the formula as $\cos(41^{\circ})=\frac{22}{XY}$, and then $XY=\frac{22}{\cos(41^{\circ})}$.

Step3: Analyze other options

The sine formula would be $\sin(41^{\circ})=\frac{XZ}{XY}$. The correct equation to solve for $XY$ using the given side $YZ$ and angle $Y$ is based on the cosine relationship.

Answer:

$XY=\frac{22}{\cos(41^{\circ})}$ (corresponding to the second option among the given choices in the image although the options are not labeled with letters in the problem statement)