Question

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

Area=1.73`units^2`

Explanation:

First you can figure out the last angle of the triangle which is `(2pi)/3` (if it helps better the angles are `15, 45, and 120` degrees.)
then you can use the law of sines to figure out another side.
`sin((2pi)/3)/4=sin(pi/4)/x`
`x=(4sin(pi/4))/sin((2pi)/3)=3.27`
then do that again to find the last side
`sin((2pi)/3)/4=sin(pi/12)/x`
`x=(4sin(pi/12))/sin((2pi)/3)=1.20`
then you can use Heron's formula.
First find S
`S=(a+b+c)/2=4.24`
then substitute
`A=sqrt(s(s-a)(s-b)(s-c))`
`A=sqrt(4.24(4.24-1.20)(4.24-4)(4.24-3.27))=1.73`