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The length of segment EF is 12 cm.

Triangle D E F is shown. Angle E D F is 90 degrees, angle D E F is 30 degrees, and angle E F D is 60 degrees. The length of hypotenuse E F is 12 centimeters.

Which statements regarding triangle DEF are correct? Select three options.

EF is the longest side of △DEF.
DF = 6 cm
DE = 12 StartRoot 3 EndRoot cm
DF = 4 StartRoot 3 EndRoot cm
DE = 6 StartRoot 3 EndRoot cm

Respuesta :

Answer:

EF is the longest side of △DEF,

DF = 6 cm and

DE = 6 StartRoot 3 EndRoot cm.

Step-by-step explanation:

The angle ∠ EDF = 90° of the right triangle Δ DEF and ∠ DEF = 30° and ∠ EFD = 60°.

The hypotenuse EF is 12 cm.

Now, Sin ∠ EFD = DE/EF

⇒ [tex]\sin 60^{\circ} = \frac{DE}{12}[/tex]

⇒ DE = 6√3 cm.

Again, Cos ∠EFD = DF/EF

⇒ [tex]\cos 60^{\circ} = \frac{DF}{12}[/tex]

⇒ DF = 6 cm.

Therefore, EF is the longest side of △DEF, DF = 6 cm and DE = 6 StartRoot 3 EndRoot cm. (Answer)

Answer: The answer is A, B, E

Step-by-step explanation:

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