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 the sine function in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, if we consider the right - triangle \(XZY\) with \(\angle Y = 41^{\circ}\), the side \(XZ = 22\) (opposite side with respect to \(\angle Y\)) and \(XY\) is the hypotenuse.

Step2: Rearrange the sine formula

We know that \(\sin(41^{\circ})=\frac{XZ}{XY}\). Since \(XZ = 22\), we can rewrite the formula as \(XY=\frac{XZ}{\sin(41^{\circ})}\). Substituting \(XZ = 22\) into the formula, we get \(XY=\frac{22}{\sin(41^{\circ})}\).

Answer:

\(XY=\frac{22}{\sin(41^{\circ})}\) (the fourth option)