Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(pi)/6`, the angle between sides B and C is `pi/3`, and the length of B is 3, what is the area of the triangle?

Answer 1

`A=9/2*sqrt(3)`

Explanation:

Since the third angle is given by

`pi-pi/6-pi/3=(6pi-pi-2pi)/6=(3pi)/6=pi/2`
so we get

`tan(pi/6)=3/a` so

`a=3/tan(pi/6)=3/(sqrt(3)/3)=9/sqrt(3)=9*sqrt(3)/3=3sqrt(3)`

So
`A=1/2*3*3*sqrt(3)=9/2*sqrt(3)`