Question

answer attempt 1 out of 2 question find the exact value of sin o in simplest radical form.

Explanation:

Step1: Recall sine - ratio definition

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $O$ in right - triangle $OPQ$, the side opposite to angle $O$ is $PQ = 3$, and the hypotenuse is $OQ=\sqrt{61}$.

Step2: Calculate $\sin O$

Using the sine - ratio formula $\sin O=\frac{PQ}{OQ}$. Substituting $PQ = 3$ and $OQ=\sqrt{61}$, we get $\sin O=\frac{3}{\sqrt{61}}$. Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{61}$, so $\sin O=\frac{3\sqrt{61}}{61}$.

Answer:

$\frac{3\sqrt{61}}{61}$