Question

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

Explanation:

Step1: Recall sine - ratio definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle M$ in right - triangle $MNO$ with right - angle at $N$, the side opposite $\angle M$ is $NO = 2$, and the hypotenuse is $MO=\sqrt{18}$.

Step2: Write the sine formula for $\angle M$

$\sin M=\frac{NO}{MO}=\frac{2}{\sqrt{18}}$.

Step3: Simplify the radical

First, simplify $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$. Then $\sin M=\frac{2}{3\sqrt{2}}$. Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{2}$: $\sin M=\frac{2\sqrt{2}}{3\times2}=\frac{\sqrt{2}}{3}$.

Answer:

$\frac{\sqrt{2}}{3}$