Question

The law of cosines is a2 +62 - 2abcosC = (2. Find the value of 2abcosC.

2
4
B
A
5

Answer 1

A. 37

Explanation:

Answer 2

`2abcosC = 37`

Explanation:

Given

`a^2 + b^2 - 2abcosC = c^2`

Required

`2abcosC`

`a^2 + b^2 - 2abcosC = c^2`

Add
`2abcosC` to both sides

`a^2 + b^2 - 2abcosC+2abcosC = c^2+2abcosC`

`a^2 + b^2 = c^2+2abcosC`

Subtract
`c^2` from both sides

`a^2 + b^2 -c^2= c^2 -c^2+2abcosC`

`a^2 + b^2 -c^2= 2abcosC`

From the attachment:

`a = 4`
`b = 5` and
`c = 2`

So, we have:

`4^2 + 5^2 -2^2= 2abcosC`

`16 + 25 -4= 2abcosC`

`37= 2abcosC`

i.e.

`2abcosC = 37`