SOLUTION: In triangle ABC, a=6, b=7, and cos C=1/4 A.) Find the exact area of the triangle. B.) Find C C.) Find sin A in simplest radical form. The part I'm having trouble with it w

Algebra ->  Triangles -> SOLUTION: In triangle ABC, a=6, b=7, and cos C=1/4 A.) Find the exact area of the triangle. B.) Find C C.) Find sin A in simplest radical form. The part I'm having trouble with it w      Log On


   

Question 193069: In triangle ABC, a=6, b=7, and cos C=1/4
A.) Find the exact area of the triangle.
B.) Find C
C.) Find sin A in simplest radical form.
The part I'm having trouble with it what does cos C=1/4 mean?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, a=6, b=7, and cos C=1/4
A.) Find the exact area of the triangle.
B.) Find C
C.) Find sin A in simplest radical form.
The part I'm having trouble with it what does cos C=1/4 mean?
Cos%28C%29=1%2F4 means that the cosine of C is 1%2F4
The formula for the area is
A+=+%28ab%2ASin%28C%29%29%2F2
So first we must find sin%28C%29 from cos%28C%29
To do this we make use of the identity Sin%5E2alpha%2BCos%5E2alpha=1
Sin%5E2C%2BCos%5E2C=1
Sin%5E2C=1-Cos%5E2C
Since we know that Cos%28C%29=1%2F4
Sin%5E2C=1-%281%2F4%29%5E2
Sin%5E2C=1-1%2F16
Sin%5E2C=16%2F16-1%2F16
Sin%5E2C=15%2F16
Sin%28C%29=sqrt%2815%2F16%29
Sin%28C%29=sqrt%2815%29%2F4
Now we can substitute in the area formula:
A+=+%28a%2Ab%2ASin%28C%29%29%2F2
A+=+%286%2A7%2A%28sqrt%2815%29%2F4%29%29%2F2
A+=+%286%2A7%2A%28sqrt%2815%29%2F4%29%29%2A%282%2F1%29
A=%286%2A7%2A2%2F4%29sqrt%2815%29
A=21sqrt%2815%29
Edwin