# Math Help - given area of triangle determine value of sin C.

1. ## given area of triangle determine value of sin C.

Triangle ABC has an area of 18cm^2. If a=5 and b=12, What does sin C equal?

2. 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!

3. I approached this problem differently. Here's my famous picture:

We know the area.

So we can derive: $\frac{12\cdot h}{2} = 18$

Simplify: $12h = 36\rightarrow h = 3$

So $Sin\,C = \frac{3}{5}$

And for the angle measure: $Sin^{-1}\big(\frac{3}{5}\big) \approx 37^o$

I'm glad me and gtbiyb agree!