given area of triangle determine value of sin C.

**jimC** · July 19th 2008, 01:23 PM

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

**gtbiyb** · July 19th 2008, 01:36 PM

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!

**Jonboy** · July 19th 2008, 01:47 PM

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!

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