In this video, I demonstrate how to use the Law of Cosines to find an unknown long side of a scalene triangle, given an angle and adjacent 2 shorter sides.
The triangle has been constructed from 2 shorter sides of lengths 2.0m and 3.0m, subtended by an angle of 135°. We are required to find the length of the longest side - and we can do that by using the Cosine Rule (aka Law of Cosines) which states...
where c is the longest side and θ is the angle between the 2 shorter sides a and b.c^2 = a^2 + b^2 - 2ab\cos \theta
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