# geometry

If a triangle has sides of lengths a and b, which make a C-degree angle, then the length
of the side opposite C is c, where c2 = a2 + b2 − 2ab cosC. This is the SAS version of the Law of Cosines. Explain the terminology. Derive an equivalent SSS version of the Law of Cosines, which gives the cosine of the angle in terms of the lengths of the three sides. Now use it to find the angles of the triangle whose sides have lengths 4 cm, 5 cm, and 6 cm.

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1. 2 a b cos C = a^2 + b^2 - c^2

cos C = [a^2 + b^2 -c^2]/2ab

a = 4
b = 5
c = 6

cos C = [ 16 + 25 - 36]/40
etc

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2. angles of 45,135,45,135

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