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: Simplify the ratio

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

Answer:

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