What is the missing angle using Law of Cosines?

[C42711]

Homework Statement

I am looking for an angle, using Law of Cosines. I am trying to solve for C.

Homework Equations

R^2= a^2+b^2- (2 X a X b X cos C)

The Attempt at a Solution

These are the numbers I am using, plugged into the Law of Cosines:
80^2= 450^2+ 373^2-(2 X 450 X 373 X cos C)
I have solved this far, Cos C= -.999
I know it's right this far, because my teacher told me it was, but I don't know how to find the angle past this point. I know I have to use inverse of cosine somehow. Please, help me, test tomorrow. Thanks.:)

 

[Chi Meson]

The cosine of an angle will give you a number (a fraction, actually) that will be between zero and 1.0 .

If you have that number (0.999 as is the case here) then you find the angle by using the inverse function. Properly, it is called the "arc-cosine" but the calculators these days use the "cos^-1" symbol.

Simply find the cos^1 of 0.999 . It's going to be a small angle, less than 5 degrees.