Triangle ABC has an area of 18cm^2. If a=5 and b=12, What does sin C equal?
I think this wants you to use the rule 1/2absinC = A, in words "the area of a triangle = 1/2 the product of two sides multipied be the sine of the angle between them so in you case 1/2 x 12 x 5sinC = 18
30sinC = 18
sinC = 3/5
C = 36.86989765 degrees
Hope that helps!
I approached this problem differently. Here's my famous picture:
We know the area.
So we can derive: $\displaystyle \frac{12\cdot h}{2} = 18$
Simplify: $\displaystyle 12h = 36\rightarrow h = 3$
So $\displaystyle Sin\,C = \frac{3}{5}$
And for the angle measure: $\displaystyle Sin^{-1}\big(\frac{3}{5}\big) \approx 37^o$
I'm glad me and gtbiyb agree!