Question

find \\(\tan(\beta)\\) in the triangle.
choose 1 answer:
a \\(\frac{5}{13}\\)
b \\(\frac{12}{13}\\)
c \\(\frac{5}{12}\\)
d \\(\frac{12}{5}\\)

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 $\beta$

For $\angle\beta$, opposite side $AC = 5$, adjacent side $BC = 12$

Step3: Calculate $\tan(\beta)$

$\tan(\beta) = \frac{AC}{BC} = \frac{5}{12}$

Answer:

C. $\frac{5}{12}$