Question

Find c.

Round to the nearest tenth.
7 ft
с
320
8 ft
c = [?]ft
Law of Cosines: c2 = a2 + b2 - 2ab cos C

Answer 1

4.2 ft

Explanation:

Given the equation for the Law of Cosines, we can rewrite the equation to solve for "c" directly:

`c^2=a^2+b^2-2ab(cosC)\\c=√(a^2+b^2-2ab(cosC))\\c=√(7^2+8^2-2(7)(8)(cos32))\\c=√(49+64-2(56)(cos32))\\c=√(113-112(cos32))\\c=√(113-94.98138677)\\c=√(18.01861323)\\c=4.244833711\\c=4.2`

So the length of c is approximately 4.2 ft