# 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?

Jan 5, 2016

The length of $a$ is $\frac{4}{3}$

#### Explanation:

We are able to solve it using logic:
Since $\frac{\pi}{8} = 2$ we'll multiply both sides by 8 resulting in $\pi = 16$.

Then, another logic: $\pi = 16$, so $\frac{\pi}{12} = \frac{16}{12} = \frac{4}{3}$.

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 $\angle C$, angle between side "b" and "c" $\angle A$ and angle between side "c" and "a" by $\angle B$.

Note:- the sign $\angle$ is read as "angle".
We are given with $\angle C$ and $\angle A$.

It is given that side $c = 2.$

Using Law of Sines
$\frac{S \in \angle A}{a} = \frac{\sin \angle C}{c}$

$\implies S \in \frac{\frac{\pi}{12}}{a} = \sin \frac{\frac{\pi}{8}}{2}$

$\implies \frac{0.2588}{a} = \frac{0.3827}{2}$

$\implies \frac{0.2588}{a} = 0.19135$

$\implies a = 1.3524$ units

Therefore, side $a = 1.3524$ units