Question

1. tan z
2. tan z

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Solve for $\tan Z$ in the first triangle

In the first right - triangle with sides $24$, $18$, and $30$, for $\angle Z$, the opposite side to $\angle Z$ is $24$ and the adjacent side is $18$. So, $\tan Z=\frac{24}{18}=\frac{4}{3}$.

Step3: Solve for $\tan Z$ in the second triangle

In the second right - triangle with sides $40$, $30$, and $50$, for $\angle Z$, the opposite side to $\angle Z$ is $40$ and the adjacent side is $30$. So, $\tan Z=\frac{40}{30}=\frac{4}{3}$.

Answer:

For the first triangle, $\tan Z = \frac{4}{3}$; for the second triangle, $\tan Z=\frac{4}{3}$