Question

question 15(multiple choice worth 4 points)
(05.03 mc)
if \\( \cos r^{\circ}=\frac{4}{9} \\) and the measure of \\( \overline{x w} \\) is 16 units, what is the measure of \\( \overline{x y} \\)?

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, in right - triangle \(XWY\) with right - angle at \(W\), \(\cos r^{\circ}=\frac{XW}{XY}\).

Step2: Substitute the known values

We are given that \(\cos r^{\circ}=\frac{4}{9}\) and \(XW = 16\) units. Let \(XY=x\). Then \(\frac{4}{9}=\frac{16}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(4x=16\times9\). So, \(4x = 144\). Divide both sides by 4: \(x=\frac{144}{4}\).

Answer:

\(36\) units.