Question

In triangle EFG, m of E = 30 degrees, m of F = 60 degrees, and m of G = 90 degrees. Which of the following statements about triangle EFG are true? Check all that apply.

A. EG = square root of 3 * FG

B. EG = 2 * FG

C. EF = square root of 3 * FG

D. EG = square root of 3 /2 * EF

E. EF = 2 * FG

F. FG = square root of 3 /2 * EF

Answer 1

A. EG = √3 × FG

D. EG = √3/2 × EF

E. EF = 2 × FG

Explanation:

apex

Answer 2

A. EG = √3 × FG

D. EG = √3/2 × EF

E. EF = 2 × FG

Explanation:

∵ tan 60 = √3

∵ tan60 = EG/GF

∴ EG/GF = √3

∴ EG = √3 × GF ⇒ A

∵ m∠F = 60°

∵ sin60 = √3/2

∵ sin 60 = EG/EF

∴ √3/2 = EG/EF

∴ EG = √3/2 × EF ⇒ D

∵ cos60 = 1/2

∵ cos60 = GF/EF

∴ GF/EF = 1/2

∴ EF = 2 × GF ⇒ E