Question

1. tan a
2. tan z
3. tan z

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Find $\tan A$

For right - triangle $ABC$ with respect to angle $A$, the opposite side to angle $A$ is $BC = 32$ and the adjacent side is $AB = 24$. So, $\tan A=\frac{BC}{AB}=\frac{32}{24}=\frac{4}{3}$.

Step3: Find $\tan Z$ for the second triangle

For right - triangle $XYZ$ with respect to angle $Z$, the opposite side to angle $Z$ is $XY = 28$ and the adjacent side is $YZ = 21$. So, $\tan Z=\frac{XY}{YZ}=\frac{28}{21}=\frac{4}{3}$.

Answer:

$\tan A=\frac{4}{3}$, $\tan Z=\frac{4}{3}$