In a right-angled triangle ABC, the height CH, equal to 3 cm, is dropped from the vertex of the right angle C.

In a right-angled triangle ABC, the height CH, equal to 3 cm, is dropped from the vertex of the right angle C. From the point H, perpendiculars HK and HL are dropped to the legs of the triangle. Find the distance between points K and L.

Segments НК and HL of the height of the triangle, drawn to the legs of the right-angled triangle ABC, therefore, the angle SKN = СLН = 90. Triangle ABC is rectangular, in which the angle ACB = 90.

Then in the quadrangle СLNK three angles are equal to 90, which means that the quadrilateral is a rectangle. The segments CH and KL are the diagonals of the rectangle, which means that the lengths are equal, KL = CH = 3 cm.

Answer: There are three centimeters between points K and L.