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 63, what is the area of the triangle?

Answer 1

`=496.125`

Explanation:

Clearly this is a right-angled triangle since Angle between sides`A` and `C` is `=pi-((5pi)/12+pi/12)`
`=pi-pi/2`
`=pi/2`
In this right angled triangle side`A` is height and side `C` is base and side `B=63` is hypotenuse
`A=height=63sin(pi/12)` and
`C= base=63cos(pi/12)`
Therefore
Area of the triangle
`=1/2times height times base`
`=1/2times63sin(pi/12)times 63cos(pi/12)`
`=1/2times63(0.2588)times 63(0.966)`
`=496.125`