The length of segment ef is 12 cm
which statements regarding triangle def are correct? select three options.

Therefore the answer is:

EF is the longest side of △DEF.

DF = 6 cm

DE=6√3

Step-by-step explanation:

The complete question is in the attached picture:

Solution:

We have to find DE .

sin60 = Perpendicular/Hypotenuse

sin60 = P/EF

sin60 = DE/EF

√3/2 = DE/12

By cross multiplication:

12(√3/2) = DE

6√3 = DE

Now we have to find DF

By applying Pythagorean Theorem

P^2 + B^2 = H^2

(6√3)^2 + B^2 = (12)^2

36(3)+B^2 = 144

108+B^2 = 144

Combine the like terms:

B^2 = 144-108

B^2 = 36

Take square root at both sides

√B^2 = √36

B= 6cm

DF= 6cm

Therefore the answer is:

EF is the longest side of △DEF.

DF = 6 cm

DE=6√3