In the right-angled triangle CDE (angle E = 90 degrees) the height EF is drawn, find СF and FD

In the right-angled triangle CDE (angle E = 90 degrees) the height EF is drawn, find СF and FD if CD = 18 cm; and the angle DCE = 30 degrees.

In a right-angled triangle CDE, the leg DE is located opposite the angle 30, then its length will be equal to half the length of the hypotenuse CD.

ED = CD / 2 = 18/2 = 9 cm.

The angle CDE = FDE = 180 – 90 – 30 = 60, then in a right-angled triangle DFE the angle FED = 180 – 90 – 60 = 30.

Then the leg DF is located opposite the angle 30, which means it is equal to half of the unit.

FD = ED / 2 = 9/2 = 4.5 cm.

The length of the segment CF = SD – FD = 18 – 4.5 = 13.5 cm.

Answer: Segment CF = 13.5 cm, segment FD is 4.5 cm.