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

Answer 1

`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