Given angles

[Dracula]

Given the 3 angles in a triangle, how do you find it's area and a unique point inside the triangle equally distant from each side ? An offshoot of Heron's formula ? THANKS.
Assume a scalene.

 

[mmm4444bot]

Given the 3 angles in a triangle, how do you find it's area

As Denis notes, the three angle-measures do not define a unique triangle.

In other words, stick your triangle into a photocopier and make a bunch of different enlargements and reductions.

Each photocopy shows a triangle with a larger or smaller area than all the rest, yet the angles on each photocopy are the same! :cool: