1. **State the problem:** We need to find the value of $\sin M$ in a right triangle $\triangle M O N$ where the right angle is at vertex $N$. The sides given are $ON = 4$ and $MO = 8$. The side $MN$ is unknown. 2. **Recall the sine definition:** In a right triangle, $\sin$ of an angle is the ratio of the length of the side opposite the angle to the hypotenuse. 3. **Identify sides relative to angle $M$:** - The hypotenuse is the side opposite the right angle, which is $MO = 8$. - The side opposite angle $M$ is $ON = 4$. 4. **Calculate $\sin M$ using the formula:** $$\sin M = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{ON}{MO} = \frac{4}{8}$$ 5. **Simplify the fraction:** $$\sin M = \frac{\cancel{4}}{\cancel{8}} = \frac{1}{2}$$ 6. **Final answer:** $$\sin M = 0.5$$ No rounding is necessary since $0.5$ is exact.