Question

determine tan(a) and tan(b).
a) tan(a)
b) tan(b)

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ to angle $\theta$.

Step2: Find $\tan(A)$

For $\angle A$, opposite side is $BC = 12$, adjacent side is $AC = 30$.
So $\tan(A) = \frac{12}{30} = \frac{2}{5}$.

Step3: Find $\tan(B)$

For $\angle B$, opposite side is $AC = 30$, adjacent side is $BC = 12$.
So $\tan(B) = \frac{30}{12} = \frac{5}{2}$.

Answer:

a) $\tan(A) = \frac{2}{5}$
b) $\tan(B) = \frac{5}{2}$