Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(5pi)/12`, the angle between sides B and C is `(5pi)/12`, and the length of B is 6, what is the area of the triangle?

Answer 1

`=33.62`

Explanation:

Since the triangle is isosceles height divides the base equally.
In other words the said triangle consists of 2 right angled triangles with base=`B/2=6/2=3` and hypotenuse =Side `A`
Therefore we can write
`A(cos((5pi)/12))=3`
or
`A(0.2588)=3`
or
`A=3/0.2588`
or
`A=11.6`
In a right angled triangle height `h=sqrt(11.6^2-3^2)=11.21`
Therefore Area of the triangle`=1/2(h)(B)`
`=1/2(11.21)(6)`
`=(11.21)(3)`
`=33.62`