Question

given right triangle pqr, which represents the value of sin(p)? options: \\(\frac{rp}{rq}\\), \\(\frac{rp}{pq}\\), \\(\frac{rq}{pq}\\), \\(\frac{rq}{pr}\\) (with a right triangle diagram labeled r (right angle), p (30°), q (60°))

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 $\angle P$

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

Step3: Substitute into sine formula

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

Answer:

$\boldsymbol{\frac{RQ}{PQ}}$ (Option C: $\frac{RQ}{PQ}$)