Question

which is the best approximation for the measure of angle xyz? 33.6° 39.8° 50.2° 56.4°

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle XYZ\), the opposite side to \(\angle XYZ\) is \(XZ = 10\) and the adjacent side is \(XY=12\). So \(\tan\angle XYZ=\frac{10}{12}=\frac{5}{6}\approx0.833\).

Step2: Use the inverse tangent function

We know that if \(\tan\alpha = x\), then \(\alpha=\tan^{- 1}(x)\). So \(\angle XYZ=\tan^{-1}(\frac{5}{6})\).
Using a calculator, \(\tan^{-1}(0.833)\approx39.8^{\circ}\)

Answer:

\(39.8^{\circ}\)