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°) xy = (22)cos(41°) xy = \frac{22}{cos(41°)} xy = \frac{22}{sin(41°)}

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, in \(\triangle XYZ\) (right - angled at \(Z\)), if we consider \(\angle Y = 41^{\circ}\), and the side adjacent to \(\angle Y\) is \(YZ\) (but since \(YZ = XZ\) (isosceles property as the non - right angles in a right - isosceles triangle have some relations, but more importantly, using the general cosine formula for a right - triangle \(\cos Y=\frac{XZ}{XY}\))

Step2: Rearrange the formula

We know that \(\cos(41^{\circ})=\frac{22}{XY}\) (where \(XZ = 22\)). Cross - multiplying gives \(XY\times\cos(41^{\circ})=22\), then \(XY=\frac{22}{\cos(41^{\circ})}\)

Answer:

\(XY=\frac{22}{\cos(41^{\circ})}\) (the third option)