A triangle has sides A, B, and C. The angle between sides A and B is #pi/8#. If side C has a length of #2 # and the angle between sides B and C is #pi/12#, what is the length of side A?

2 Answers
Jan 5, 2016

The length of #a# is #4/3#

Explanation:

We are able to solve it using logic:
Since #pi/8 = 2# we'll multiply both sides by 8 resulting in #pi = 16#.

Then, another logic: #pi = 16#, so #pi/12 = 16/12 = 4/3#.

I won't say units, its implicit.

Jan 5, 2016

#a=1.3524# 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=2.#

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

#implies Sin(pi/12)/a=sin((pi)/8)/2#

#implies 0.2588/a=0.3827/2#

#implies 0.2588/a=0.19135#

#implies a=1.3524# units

Therefore, side #a=1.3524# units