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: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(YZX\), the opposite side is \(XY\) and the hypotenuse is \(YZ\).

Step2: Calculate \(\sin(\angle YZX)\)

We know \(XY = 12.4\) and \(YZ=15.1\). So, \(\sin(\angle YZX)=\frac{XY}{YZ}=\frac{12.4}{15.1}\approx0.8212\).

Step3: Find the angle using the inverse sine function

\(\angle YZX=\sin^{- 1}(0.8212)\). Using a calculator, \(\sin^{-1}(0.8212)\approx55.2^{\circ}\).

Answer:

\(55.2^{\circ}\)