Question

find the tangent of ∠q.
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
tan(q) =

Explanation:

Step1: Recall tangent formula

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

Step2: Identify side lengths

We are given that $QS = 20$ and $SR=52$.

Step3: Calculate tangent

$\tan(Q)=\frac{SR}{QS}=\frac{52}{20}$.

Step4: Simplify the fraction

$\frac{52}{20}=\frac{13}{5}$.

Answer:

$\frac{13}{5}$