Question

The law of cosines is a^2+b^2-2abcos(C). Find the value of 2abcos(C).

A. 37
B. -40
C. 40
D. 20​

Answer 1

A. 37

Explanation:

Given

The attached triangle and

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

Required

Find
`2abcos(C)`

From the attachment:

`a = 4`

`b = 5`

`c = 2`

So, we have:

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

`2^2=4^2 + 5^2 -2abcos(C)`

`4=16 + 25 -2abcos(C)`

Collect like terms

`2abcos(C)=16 + 25 -4`

`2abcos(C)=37`