Question

identifying trig ratios (no diagram)
question
in \\( \triangle \mathrm { pqr } \\), the measure of \\( \angle \mathrm { r } = 90 ^ { \circ } \\), \\( \mathrm { rq } = 80 \\), \\( \mathrm { pr } = 39 \\), and \\( \mathrm { qp } = 89 \\). what ratio represents the sine of \\( \angle \mathrm { p } \\)?
answer
attempt 1 out of 3
submit answer

Explanation:

Step1: Recall the sine ratio formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify the sides relative to $\angle P$

For $\angle P$ in $\triangle PQR$ with $\angle R = 90^{\circ}$, the side opposite to $\angle P$ is $RQ$ and the hypotenuse is $QP$.

Step3: Substitute the values into the formula

We have $RQ = 80$ and $QP=89$. So, $\sin P=\frac{RQ}{QP}$.

Answer:

$\frac{80}{89}$