Question

The law of cosines is a^2+b^2-2abcosC=c^2. Find the value of 2abcosC.

Answer 1

2ab x cos (C) = 7 because

a^2 + b^2 - 2ab x cos(C) = c^2
2ab x cos(C) = a^2 + b^2 - c^2
2ab x cos(C) = 2^2 + 2^2 - 1^2
2ab x cos (C) = 7

Answer 2

(D)
`7=2abcosC`

Explanation:

It is given from figure that c=1, a=2 and b=2, thus using the law of cosines, we get

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

Substituting the given values, we get

`(1)^2=(2)^2+(2)^2-2abcosC`

`1=4+4-2abcosC`

`1=8-2abcosC`

`1-8=-2abcosC`

`-7=-2abcosc`

`7=2abcosC`

Thus, the value of
`2abcosC` is
`7`.

Hence, option (D) is correct.