Question

find xy.
write your answer as an integer or as a decimal rounded to the nearest tenth.
xy =

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(WXY\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 22^{\circ}\), the adjacent side to \(\angle Y\) is \(XY\), and the hypotenuse \(WY=\sqrt{41}\).

Step2: Apply the cosine formula

We know that \(\cos Y=\frac{XY}{WY}\). Substituting \(Y = 22^{\circ}\) and \(WY=\sqrt{41}\), we get \(XY = WY\times\cos(22^{\circ})\).
Since \(\cos(22^{\circ})\approx0.9272\) and \(WY=\sqrt{41}\approx6.4031\).

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Answer:

\(XY = 6.0\)