Answer:
[tex]2abcosC = 37[/tex]
Step-by-step explanation:
Given
[tex]a^2 + b^2 - 2abcosC = c^2[/tex]
Required
[tex]2abcosC[/tex]
[tex]a^2 + b^2 - 2abcosC = c^2[/tex]
Add [tex]2abcosC[/tex] to both sides
[tex]a^2 + b^2 - 2abcosC+2abcosC = c^2+2abcosC[/tex]
[tex]a^2 + b^2 = c^2+2abcosC[/tex]
Subtract [tex]c^2[/tex] from both sides
[tex]a^2 + b^2 -c^2= c^2 -c^2+2abcosC[/tex]
[tex]a^2 + b^2 -c^2= 2abcosC[/tex]
From the attachment:
[tex]a = 4[/tex] [tex]b = 5[/tex] and [tex]c = 2[/tex]
So, we have:
[tex]4^2 + 5^2 -2^2= 2abcosC[/tex]
[tex]16 + 25 -4= 2abcosC[/tex]
[tex]37= 2abcosC[/tex]
i.e.
[tex]2abcosC = 37[/tex]
