Question

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 `1` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

`a=0.2679` 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=1.`

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

`implies Sin(pi/12)/a=sin((7pi)/12)/1`

`implies 0.2588/a=0.9659`

`implies a=0.2588/0.9659=0.2679`

`implies a=0.2679` units

Therefore, side `a=0.2679` units