Question

4 multiple choice 1 point write the tangent ratios for $\angle y$ and $\angle z$. not drawn to scale $\tan y=\frac{\sqrt{65}}{7},\tan z=\frac{\sqrt{65}}{4}$ $\tan y=\frac{7}{\sqrt{65}},\tan z=\frac{4}{\sqrt{65}}$ $\tan y=\frac{4}{7},\tan z=\frac{7}{4}$ $\tan y=\frac{7}{4},\tan z=\frac{4}{7}$

Explanation:

Step1: Recall the tangent ratio formula

The tangent of an angle in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Find \(\tan Y\)

For \(\angle Y\), the side opposite is \(XZ = 7\) and the side adjacent is \(XY = 4\). So \(\tan Y=\frac{XZ}{XY}=\frac{7}{4}\).

Step3: Find \(\tan Z\)

For \(\angle Z\), the side opposite is \(XY = 4\) and the side adjacent is \(XZ = 7\). So \(\tan Z=\frac{XY}{XZ}=\frac{4}{7}\).

Answer:

\(\tan Y=\frac{7}{4},\tan Z=\frac{4}{7}\)