Question

in right triangle xyz, the right angle is located at vertex y. the length of line segment xy is 12.4 cm. the length of line segment yz is 15.1 cm. which is the approximate measure of angle yzx? 34.8° 39.4° 50.6° 55.2°

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(XYZ\) with right - angle at \(Y\), we want to find \(\angle YZX\). We know the opposite side (\(XY\)) and the adjacent side (\(YZ\)) with respect to \(\angle YZX\). The tangent ratio is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(\angle YZX)=\frac{XY}{YZ}\).

Step2: Substitute the given values

Given \(XY = 12.4\) cm and \(YZ=15.1\) cm. Then \(\tan(\angle YZX)=\frac{12.4}{15.1}\approx0.8212\).

Step3: Find the angle

To find \(\angle YZX\), we take the inverse - tangent (arctan) of \(0.8212\). So, \(\angle YZX=\arctan(0.8212)\). Using a calculator, \(\angle YZX\approx39.4^{\circ}\).

Answer:

39.4°