In a right-angled triangle CDE with a right angle E, the height EH is drawn. find CH and HD

In a right-angled triangle CDE with a right angle E, the height EH is drawn. find CH and HD if CD is 18 cm and DCE is 30 degrees.

1. Calculate the value of the CDE angle:

180 ° – 90 ° – 30 ° = 60 °

2. In a right-angled triangle DEН, the leg EH is opposite the angle CDE, equal to 60, DE is the hypotenuse. Their ratio is equal to the sine of the СDE angle (√3 / 2).

EH / DE = √3 / 2; EH = 9 x √3 / 2 = 4.5√3 cm.

3. Angle DEН = 180 ° – 90 ° – 60 ° = 30 °.

3. In a right-angled triangle DEН, the leg DН is opposite an angle equal to 30 °, therefore it is equal to half of the hypotenuse DE.

DН = DE / 2 = 9/2 = 4.5 cm.

4.CH = 18 – 4.5 = 13.5 cm.

Answer: CH = 13.5 cm, DН = 4.5 cm.