Answer:
Correct: A, D, F
Step-by-step explanation:
Consider right triangle EFG.
By the definition of the cosine function,
[tex]\cos \angle E=\dfrac{EG}{EF}\\ \\\cos 30^{\circ}=\dfrac{EG}{EF}\\ \\\dfrac{\sqrt{3}}{2}=\dfrac{EG}{EF}\\ \\EG=\dfrac{\sqrt{3}}{2}EF[/tex]
Option F is correct.
By the definition of the sine function,
[tex]\sin \angle E=\dfrac{FG}{EF}\\ \\\sin 30^{\circ}=\dfrac{GF}{EF}\\ \\\dfrac{1}{2}=\dfrac{GF}{EF}\\ \\GF=\dfrac{1}{2}EF\\ \\EF=2FG[/tex]
Option D is correct.
By the definition of tangence,
[tex]\tan \angle E=\dfrac{FG}{EG}\\ \\\tan 30^{\circ}=\dfrac{GF}{EGF}\\ \\\dfrac{1}{\sqrt{3}}=\dfrac{GF}{EG}\\ \\GF=\dfrac{1}{\sqrt{3}}EGF\\ \\EG=\sqrt{3}FG[/tex]
Option A is correct
