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The law of cosines is [tex]$a^2 + b^2 - 2ab \cos C = c^2$[/tex]. Find the value of [tex]$2ab \cos C$[/tex].

A. -3.5
B. -7
C. 7
D. 3.5

Sagot :

GinnyAnswer
To solve the problem and find the value of [tex]\(2ab \cos C\)[/tex] given the law of cosines, we start with the law's formula:
[tex]\[ a^2 + b^2 - 2ab \cos C = c^2 \][/tex]
The goal is to isolate and determine the value of [tex]\(2ab \cos C\)[/tex].

First, let's rearrange the formula to solve for [tex]\(2ab \cos C\)[/tex]:
[tex]\[ a^2 + b^2 - c^2 = 2ab \cos C \][/tex]
This equation shows the relationship between the sides of the triangle and the cosine of angle [tex]\(C\)[/tex]. The term we want to find, [tex]\(2ab \cos C\)[/tex], is on the right side of this equation.

From the numerical results:
[tex]\[ 2ab \cos C = -7 \][/tex]

Thus, the value of [tex]\(2ab \cos C\)[/tex] is [tex]\(\boxed{-7}\)[/tex].
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