Question

ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?

Answer 1

C I got this question right on my test that I just finished.

Explanation:

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Answer 2

`cos(C) =(40)/(41)\\\\cos(C)=0.976`

Explanation:

To find the
`cos (C)` we must use the cosine theorem.

The cosine theorem says that:

`c^2 = a^2 +b^2 -2abcos(C)`

In this case:

`c=AB = 9`

`b=CA = 41`

`a=BC = 40`

So

`9^2 = 40^2 +41^2 -2(40)*(41)cos(C)`

`9^2- 40^2- 41^2 =-2(40)*(41)cos(C)`

`cos(C) = -(9^2- 40^2- 41^2)/(2(40)*(41))`

`cos(C) =(40)/(41)\\\\cos(C)=0.976`