Question

1. for the right triangle $\delta abc$ shown below, what is $\tan b$?

f. $\dfrac{a}{b}$
g. $\dfrac{a}{c}$
h. $\dfrac{b}{a}$
j. $\dfrac{c}{a}$
k. $\dfrac{c}{b}$

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$.

Step2: Identify sides for $\angle B$

• Opposite side to $\angle B$: $c$
• Adjacent side to $\angle B$: $a$

Step3: Compute $\tan B$

$\tan B = \frac{\text{opposite}}{\text{adjacent}} = \frac{c}{a}$

Answer:

J. $\frac{c}{a}$