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 $Y$, to find $\angle YZX$, we use the tangent ratio. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the side opposite to $\angle YZX$ is $XY$ and the side adjacent to $\angle YZX$ is $YZ$. 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

We know that if $\tan\theta = 0.8212$, then $\theta=\arctan(0.8212)$. Using a calculator, $\angle YZX=\arctan(0.8212)\approx39.4^{\circ}$.

Answer:

$39.4^{\circ}$