Question

A triangle has sides A, B, and C. The angle between sides A and B is `(3pi)/4` and the angle between sides B and C is `pi/12`. If side B has a length of 4, what is the area of the triangle?

Answer 1

`S=4sqrt(4-sqrt6)`

Explanation:

The angle between A and C is `pi-3pi/4-pi/12=pi/6`
Acording theorem of sin length C: `C/sin(3pi/4)=4/sin(pi/6)`
`C=4sqrt2`
Area of the triangle: `S=BCsin(pi/12)/2`
`sin(pi/12)=sqrt((1-cos(pi/6))/2)`
`sin(pi/12)=sqrt(2-sqrt3)/2`