Question

A triangle has sides A, B, and C. The angle between sides A and B is `(2pi)/3` and the angle between sides B and C is `pi/12`. If side B has a length of 12, what is the area of the triangle?

Answer 1

37.5034

Explanation:

First, we find the missing angle `pi/12` is 15 degrees and `(2pi)/3` is 120 all triangle's angles add up to 180 180-135 and the missing angle is 45 degrees or `pi/4` now that there is a known side, we can use the sin rule.
`a/(sin A) = b/sin B = c/sinC`
`c=(bsinC)/sinb`

`(12 sin 120)/ sin 45` is 8.188160008 side C
for the next side we get 9.170785943 ide A
http://www.teacherschoice.com.au/Maths_Library/Trigonometry/solve_trig_AAS.htm for more details

the area is 37.5034
here is a good online calculator for this
https://www.mathopenref.com/heronsformula.html
and also how I got to this area.