Question

given right triangle abc, what is the value of tan(a)?
$\frac{5}{13}$
$\frac{12}{13}$
$\frac{12}{5}$
$\frac{13}{12}$

Explanation:

Step1: Recall tangent definition

For angle $A$, $\tan(A) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $\angle A$

Opposite side to $\angle A$ is $BC=24$, adjacent side is $AC=10$

Step3: Calculate $\tan(A)$

$\tan(A) = \frac{24}{10} = \frac{12}{5}$

Answer:

$\boldsymbol{\frac{12}{5}}$ (corresponding to the option $\boldsymbol{\frac{12}{5}}$)