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 $A$ in right triangle, $\tan(A)=\frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify opposite/adjacent sides

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

Step3: Simplify the fraction

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

Answer:

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