Question

given right triangle pqr, which represents the value of sin(p)?
option 1: \\(\frac{rp}{rq}\\)
option 2: \\(\frac{rp}{pq}\\)
option 3: \\(\frac{rq}{pq}\\)
option 4: \\(\frac{rq}{pr}\\)

Explanation:

Step1: Recall Sine Definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle P$ (30°), identify opposite and hypotenuse.

Step2: Identify Sides

• Opposite to $\angle P$: $RQ$ (side opposite 30° angle).
• Hypotenuse: $PQ$ (longest side, opposite right angle at $R$).

Step3: Apply Sine Formula

$\sin(P) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{RQ}{PQ}$.

Answer:

$\boldsymbol{\frac{RQ}{PQ}}$ (corresponding option: the one with $\frac{RQ}{PQ}$)