Question

khan academy
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 the tangent formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify the opposite and adjacent sides for angle $\beta$

For angle $\beta$, the opposite side is $AC = 5$ and the adjacent side is $BC=12$.

Step3: Calculate $\tan(\beta)$

Using the formula $\tan(\beta)=\frac{AC}{BC}$, we substitute $AC = 5$ and $BC = 12$. So, $\tan(\beta)=\frac{5}{12}$.

Answer:

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