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 side opposite to \(\angle XYZ\) is \(XZ = 10\) in and the side adjacent to \(\angle XYZ\) is \(XY=12\) in. So, \(\tan x=\frac{10}{12}\).

Step2: Simplify the ratio

\(\frac{10}{12}=\frac{5}{6}\approx0.833\).

Step3: Find the angle using the inverse tangent function

\(x = \tan^{-1}(0.833)\). Using a calculator, \(\tan^{-1}(0.833)\approx39.8^{\circ}\).

Answer:

\(39.8^{\circ}\)