What is the trigonometric ratio for sin c ?

enter your answer, as a simplified fraction.

By definition we have to:
 Sin (x) = C.O / h
 Where,
 x = angle
 C.O = opposite leg
 h: hypotenuse.
 Substituting values we have:
 Sin (C) = AB / 82
 We should look for AB. For this, we use the following relationship:
 AB ^ 2 + 80 ^ 2 = 82 ^ 2
 Clearing AB:
 AB = root ((82 ^ 2) - (80 ^ 2))
 AB = 18
 Substituting we have:
 Sin (C) = 18/82
 Simplifying:
 Sin (C) = 9/41

 
 the trigonometric ratio for sin C is:
 Sin (C) = 9/41

Why are u not just putting the numbers this is to much