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.

a. length of segment ED is 10.39 cm

b. length of segment DF if 6 cm

c. triangle DEF is an scalene triangle (that is a triangle with no equal sides)

Step-by-step explanation:

using the trigonometric identities SOHCAHTOA; which means

sin = opposite/hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

from the triangle; if the length of segment EF is the hypotenuse (the longest side) then

1. length of ED (the side opposite the angle 60)

sin = opposite / hypotenuse

sin = a /12

a = 12 sin

a = 10.39 cm

2. length of DF (the side opposite the angle 30)

sin = opposite / hypotenuse

sin = b /12

b = 12 sin 30

b = 6 cm

3. from the two answers above it is easy to see that the length of all the sides of the triangle DEF are not the same and this kind of triangle is called a scalene triangle

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.