Question

find tan(β) in the triangle. choose 1 answer: a $\frac{8}{17}$ b $\frac{15}{17}$ c $\frac{8}{15}$ d $\frac{15}{8}$

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, for an acute angle $\beta$, $\tan(\beta)=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify opposite and adjacent sides

For angle $\beta$ in right - triangle $ABC$, the side opposite to $\beta$ is $AC = 8$ and the side adjacent to $\beta$ is $BC = 15$.

Step3: Calculate $\tan(\beta)$

$\tan(\beta)=\frac{AC}{BC}=\frac{8}{15}$

Answer:

C. $\frac{8}{15}$