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 the definition of sine in a right - triangle

In a right - triangle, for an acute angle $\theta$, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify the sides relative to angle $P$

For angle $P$ in right - triangle $PQR$, the side opposite to angle $P$ is $RQ$, and the hypotenuse is $PQ$.

Step3: Apply the sine formula

By the formula $\sin(P)=\frac{\text{opposite}}{\text{hypotenuse}}$, substituting the values of the sides, we get $\sin(P)=\frac{RQ}{PQ}$.

Answer:

$\frac{RQ}{PQ}$