Even if a diagram is not given, if you visualize it, EDG forms a right triangles with a bisector line DF. FG is then the lower half of segment EFG. To determine FG, use trigonometric functions like sine, cosine or tangent to relate the sides. For FG, you could use
tan ∅/2 = FG/DG
FG = DG tan(∅/2)
The angle is denoted as ∅/2 because of the angle bisector. DG is the base of the right triangle.