Question

14
given the following triangle rsq, find tan q.
r 36 s
39
q

Explanation:

Step1: Recall the tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $Q$, the side opposite to $Q$ is $RS = 36$, and the side adjacent to $Q$ is $SQ=15$.

Step2: Calculate $\tan Q$

$\tan Q=\frac{RS}{SQ}=\frac{36}{15}=\frac{12}{5}$ (simplify the fraction by dividing both numerator and denominator by 3).

Answer:

$\frac{12}{5}$