Question

Express sin M as a fraction in simplest terms

Answer 1

Remember: SOH-CAH-TOA

Sine (of an angle!) = opposite / hypotenuse

We're looking at angle M here, to find the sine of M. Looking from angle M, the side that is opposite is NO and the hypotenuse is MO.

sin(M) = NO / MO = NO / 13

We do not know NO, but we can use the Pythagorean theorem to find NO because this is a right triangle.

Pythagorean theorem: a^2 + b^2 = c^2

---a and b are legs of the triangle, c is the hypotenuse

12^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 5

NO = 5

sin(M) = NO / MO = 5 / 13

Answer: sin(M) = 5 / 13

Hope this helps!