In a right-angled triangle DBC (LC = 90), the height of the CK was drawn. Find the segment DK if DB = 20 cm, BC = 10 cm.

1. The leg BC is equal to 1/2 of the hypotenuse DB, which means that the angle D opposite which it lies is equal to 30 degrees. Hence the angle in = 90 – 30 = 60 degrees (the sum of the acute angles in a rectangular triangle is 90 degrees)
2. Consider a triangle CBK – rectangular (angle K = 90 degrees, since the CK is the height given)
1) The CKB angle will be 90 – 60 = 30 degrees.
2) The BK leg lies opposite an angle of 30 degrees, which means that it is equal to half of the BC hypotenuse. BC = 10, so BC = 5 cm
Answer: BK = 5 cm.