Question

A triangle has sides A, B, and C. The angle between sides A and B is `(2pi)/3`. 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

`color(green)(a = ( c sin A ) / sin C = (16 * sin (pi/12)) / sin ((2pi)/3) ~~ 4.78`

Explanation:

Law of sines

Given : c = 16, hat C = (2pi)/3, hat A = pi/12#

To find length of side `color(green)(a`

Applying Law of Sines,

`color(green)(a = ( c sin A ) / sin C = (16 * sin (pi/12)) / sin ((2pi)/3) ~~ 4.78`