Question

question in △qrs, the measure of ∠s = 90°, rq = 97, qs = 72, and sr = 65. what ratio represents the tangent of ∠r? answer attempt 1 out of 2

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, for an acute angle $\theta$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In right - triangle $\triangle QRS$ with $\angle S = 90^{\circ}$, for $\angle R$, the side opposite to $\angle R$ is $QS$ and the side adjacent to $\angle R$ is $SR$.

Step2: Calculate the tangent of $\angle R$

$\tan R=\frac{QS}{SR}$. Given $QS = 72$ and $SR=65$, so $\tan R=\frac{72}{65}$.

Answer:

$\frac{72}{65}$