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Length of a side of triangle (with the lengths of two sides and their containes angle known)

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When the lengths (a, b) of two sides and their contained angle (C) for a trangle are known as shown in figure, length (c) of the other side can be determined as follows. 

Drawing a perpendicular line from point B
to the side b,  it becomes the height whose length is a*sin(C).

The side b is the sum of two parts a*cos(C) and b-a*cos(C) as shown in figure.

By Pithagorean theorem,

c^2 = (a*sin(C))^2 + (b-a*cos(C))^2  

or

c = ((a*sin(C))^2 + (b-a*cos(C))^2)^(1/2)

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c = ((a*sin(C))^2 + (b-a*cos(C))^2)^(1/2)
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