A triangle has sides A, B, and C. The angle between sides A and B is #(7pi)/12#. If side C has a length of #16 # and the angle between sides B and C is #pi/12#, what is the length of side A?

1 Answer
SagarStudy · Júlio B.
Jan 5, 2016

#a=4.28699# units

Explanation:

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#, angle between side "b" and "c" #/_ A# and angle between side "c" and "a" by #/_ B#.

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

It is given that side #c=16.#

Using Law of Sines
#(Sin/_A)/a=(sin/_C)/c#

#implies Sin(pi/12)/a=sin((7pi)/12)/16#

#implies 0.2588/a=0.9659/16#

#implies 0.2588/a=0.06036875#

#implies a=0.2588/0.06036875=4.28699 implies a=4.28699 # units

Therefore, side #a=4.28699# units

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