which is the best approximation for the measure of angle xyz? 33.6° 39.8° 50.2° 56.4°
which is the best approximation for the measure of angle xyz? 33.6° 39.8° 50.2° 56.4°
Answer
Explanation:
Step1: Identify the trig - ratio
In right - triangle $XYZ$ with right - angle at $X$, we know the adjacent side to $\angle XYZ$ is $XY = 12$ inches and the opposite side is $XZ=10$ inches. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(\angle XYZ)=\frac{XZ}{XY}$.
Step2: Calculate the tangent value
Substitute $XZ = 10$ and $XY = 12$ into the formula: $\tan(\angle XYZ)=\frac{10}{12}=\frac{5}{6}\approx0.8333$.
Step3: Find the angle
We know that if $\tan\theta = 0.8333$, then $\theta=\arctan(0.8333)$. Using a calculator in degree mode, $\angle XYZ=\arctan(0.8333)\approx39.8^{\circ}$.
Answer:
39.8°