Question

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

Answer 1

Answer: The answer is A, B, E

Explanation:

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Answer 2

EF is the longest side of △DEF,

DF = 6 cm and

DE = 6 StartRoot 3 EndRoot cm.

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

⇒
`\sin 60^(\circ) = (DE)/(12)`

⇒ DE = 6√3 cm.

Again, Cos ∠EFD = DF/EF

⇒
`\cos 60^(\circ) = (DF)/(12)`

⇒ DF = 6 cm.

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