Question

given right triangle pqr, which represents the value of sin(p)? \\(\frac{rp}{rq}\\) \\(\frac{rp}{pq}\\) \\(\frac{rq}{pq}\\) \\(\frac{rq}{pr}\\)

Explanation:

Step1: Recall sine definition

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$.

Step2: Identify sides for $\angle P$

In $\triangle PQR$, right-angled at $R$:

• Opposite side to $\angle P$: $RQ$
• Hypotenuse: $PQ$

Step3: Substitute into sine formula

$\sin(P) = \frac{RQ}{PQ}$

Answer:

$\boldsymbol{\frac{RQ}{PQ}}$ (the third option)