Question

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?

Answer 1

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.

Answer 2

`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