The value of sin M is 3/5.
To express the sine of angle M as a fraction in simplest terms, we need to find the ratio of the opposite side to the hypotenuse.
Given that sin M = 3/5 and MNO is a right angle triangle with MN = 24 and NO = 18, we can use the Pythagorean theorem to find the length of the hypotenuse MO.
Using the Pythagorean theorem, we have:
MO² = MN² + NO²
MO² = 24² + 18²
MO² = 576 + 324
MO² = 900
MO = 30
Now, we can use the definition of sine to find the value of sin M:
sin M = opposite/hypotenuse
sin M = NO/MO
sin M = 18/30
sin M = 3/5
Therefore, the value of sin M is 3/5.