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Question

For the following triangle, find angle C, a=4, b=5, c=7

Answer 1

use the Law of Cosines

It's a modified version of the Pythagorean Theorem for triangles that aren't right triangles

c^2 = a^2 +b^2 -2abCosC

c=7, a=4, b=5

49 = 16+25 -2(4)(5)CosC

CosC = (49-41)/40 = 8/40 = 1/5 = .2

CosC = .2

use a calculator with an inverse cosine function

C = Cos^-1(.2) = about 78.46 degrees