Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/12` 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

pl,see below

Explanation:

The angle between sides A and B `=5pi/12`
The angle between sides C and B `=pi/12`
The angle between sides C and A `=pi -5pi/12-pi/12=pi/2`
hence the triangle is right angled one and B is its hypotenuse.
Therefore side A = `Bsin(pi/12)=4sin(pi/12)`
side C = `Bcos(pi/12)=4cos(pi/12)`
So area`= 1/2ACsin(pi/2)=1/2*4sin(pi/12)*4cos(pi/12)`
`=4*2sin(pi/12)*cos(pi/12)`
`=4*sin(2pi/12)`
`=4*sin(pi/6)`
`=4*1/2` =2 sq unit