A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 9, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

1 Answer
Alan P.
Dec 16, 2016

abs(C)~~color(green)(10.3793)

Explanation:

The Law of Cosines tells us that
color(white)("XXX")abs(C)=sqrt(abs(A)^2+abs(B)^2-2abs(A)abs(B)cos(c))
where c is the angle opposite side C (i.e. the angle between A and B)

abs(C)=sqrt(8^2+9^2-2 * 8 * 9 *cos((5pi)/12))

using a calculator (or spreadsheet) should (if I haven't messed up) give the answer above.

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