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

Answer 1

`A=(6sin(pi/12))/sin(pi/8)~=4.06`

Explanation:

We can use the the Law of sines, which states that the ratio of the length of a side to the sine of its opposite angle is equal for all sides and angles in a triangle. You can also express this using the following equation:

`sin(alpha)/a=sin(beta)/b=sin(gamma)/c`

where `alpha` is the opposite side to `a`, `beta` is the opposite side to `b` and `gamma` is the opposite side to `c`.

If you draw up the triangle, you can see that `pi/8` is the angle opposite `C` and `pi/12` is the angle opposite `A`. Using the Law of sines, we can setup the following equation:

`sin(pi/8)/6=sin(pi/12)/A`

`Asin(pi/8)=6sin(pi/12)` (using cross-multiplication)

`A=(6sin(pi/12))/sin(pi/8)~=4.06`