Question

Solve for triangle EFG given that g = 5, e = 7, and G = 43°. If no solution exists, select "none."

a.f = 6.6, E = 72.7°, and F = 64.3°, or f = 3.6, E = 107.3°, and F = 29.7°
b.f = 7.9, E = 24.2°, and F = 112.8°
c.f = 6.6, E = 63.4°, and F = 73.6°, or f = 9.2, E = 116.6°, and F = 20.4°
d.none

Answer 1

so my opinion that if you see it this draw and check the added datets in the text of your exercise you can deducting that

to angle G = 43 ° is added the side EF with length g=5

so if you check after this the draw you can dedicting that f > g so f > 5
what mean that the angle added to side with length f need being greater than
angle G = 43°

so if i check your draw i need saying that this not is right --- sorry my opinion

Answer 2

you can use "sine rule" to get the angle E
then the fact that sum of all internal angles of a triangle = 180, you can get the thrid angle "F"