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

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

⇒

⇒ DE = 6√3 cm.

Again, Cos ∠EFD = DF/EF

⇒

⇒ DF = 6 cm.

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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.