Question

Please help! tysm i really appreciate it!

Answer 1

Correct: A, D, F

Explanation:

Consider right triangle EFG.

By the definition of the cosine function,

`\cos \angle E=(EG)/(EF)\\ \\\cos 30^(\circ)=(EG)/(EF)\\ \\(√(3))/(2)=(EG)/(EF)\\ \\EG=(√(3))/(2)EF`

Option F is correct.

By the definition of the sine function,

`\sin \angle E=(FG)/(EF)\\ \\\sin 30^(\circ)=(GF)/(EF)\\ \\(1)/(2)=(GF)/(EF)\\ \\GF=(1)/(2)EF\\ \\EF=2FG`

Option D is correct.

By the definition of tangence,

`\tan \angle E=(FG)/(EG)\\ \\\tan 30^(\circ)=(GF)/(EGF)\\ \\(1)/(√(3))=(GF)/(EG)\\ \\GF=(1)/(√(3))EGF\\ \\EG=√(3)FG`

Option A is correct