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

Answer:

4.2 ft

Step-by-step explanation:

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

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

So the length of c is approximately 4.2 ft