Answer: Choice C) 3/5
Angle NOM, or angle O for short if you just focus on triangle NOM (ignore point L), has the side MN = 3 opposite this reference angle. The hypotenuse is MO = 5 units. This is found through the pythagorean theorem
a^2+b^2 = c^2
3^2+4^2 = c^2
25 = c^2
c^2 = 25
c = sqrt(25)
c = 5
Triangle NOM is a 3-4-5 right triangle. The ratio of the opposite and hypotenuse will get us the sine of angle NOM
so,
sin(angle NOM) = opposite/hypotenuse
sin(angle NOM) = MN/MO
sin(angle NOM) = 3/5
note: we do not use point L at all, nor do we use the fact that LM = 12 To avoid potential confusion, it might be best to draw out triangle NOM only with the proper labels as you see in the diagram below (see attached image).
