A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #6#, respectively, and the angle between A and B is #(5pi)/8 #. What is the length of side C?

1 Answer
Miguel F.
Jan 1, 2016

This problem may be solved easily by using the law of cosines.

Explanation:

Given a triangle, with sides #a#, #b# and #c#, and angles #alpha#, #beta# and #gamma# (best see the figure below), we can calculate the length of a given side by knowing the lengths of the other two, and the angle between them.

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For example, to calculate the length of #c#:

#c^2 = a^2 + b^2 - 2 a b cos gamma#

In our case:

#c^2 = 7^2 + 6^2 - 2 cdot 7 cdot 6 cdot cos {5 pi}/8 = 117.15#
#rightarrow c = sqrt{117.15} = 10.82#

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