A triangle has sides A, B, and C. Sides A and B are of lengths #1# and #7#, respectively, and the angle between A and B is #(2pi)/3 #. What is the length of side C?

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Answer 1 · 2016-01-08T17:01:55

#7.5498# units.

First of all let me denote the sides with small letters #a#, #b# and #c#
Let me name the angle between side "a" and "b" by #/_ C#.

Note:- the sign #/_# is read as "angle".
We are given with #/_C#

It is given that #a=1# and #b=7#

Using Law of Cosines
#c^2=a^2+b^2-2abcos/_C#

#c^2=1^2+7^2-2*1*7cos((2pi)/3)#

#implies c^2=1+49-14cos((2pi)/3)#

#implies c^2=50-14(-0.5)=50+7=57#
#implies c^2=57 implies c=7.5498# units.