Question

5 multiple choice 1 point
write the tangent ratios for \\( \angle y \\) and \\( \angle z \\).
not drawn to scale
\\( \tan y=\frac{2}{3}, \tan z=\frac{3}{2} \\)
\\( \tan y=\frac{\sqrt{13}}{3}, \tan z=\frac{\sqrt{13}}{2} \\)
\\( \tan y=\frac{3}{\sqrt{13}}, \tan z=\frac{2}{\sqrt{13}} \\)
\\( \tan y=\frac{3}{2}, \tan z=\frac{2}{3} \\)

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 opposite side is $2$ and the adjacent side is $3$. So, $\tan Y=\frac{2}{3}$.

Step3: Find $\tan Z$

For $\angle Z$, the opposite side is $3$ and the adjacent side is $2$. So, $\tan Z=\frac{3}{2}$.

Answer:

$\tan Y=\frac{2}{3},\tan Z=\frac{3}{2}$ (the first option)