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Mathematics

Answered

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

Find C Round To The Nearest Tenth 7 Ft С 320 8 Ft C Ft Law Of Cosines C2 A2 B2 2ab Cos C class=

Answer :

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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:

[tex]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[/tex]

So the length of c is approximately 4.2 ft

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