Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that in right - triangle $XYZ$ with right - angle at $X$, $\tan\angle Y=\frac{opposite}{adjacent}=\frac{XZ}{XY}$. Here, $XZ = 10$ in and $XY=12$ in. So, $\tan\angle Y=\frac{10}{12}=\frac{5}{6}$.

Step2: Find the angle

We use the inverse - tangent function, $\angle Y=\tan^{- 1}(\frac{5}{6})$. Using a calculator, $\angle Y=\tan^{-1}(\frac{5}{6})\approx39.8^{\circ}$.

Answer:

$39.8^{\circ}$