The larger leg of a right-angled triangle is 20 and the projection of the legs to the hypotenuse is 16: 9

The larger leg of a right-angled triangle is 20 and the projection of the legs to the hypotenuse is 16: 9 find the distance from the base of the height to the hypotinus to the smaller leg.

The desired distance HK is the height drawn from the point H to the smaller base.

Triangles ABC and KHB are rectangular and similar in acute angle B.

Let the length of the segment BH = 9 * X cm, then, by condition, the length of the segment AH = 15 * X. The length of the hypotenuse AB = AH + BH = 16 * X + 9 * X = 25 * X.

Then: AC / HK = AB / BH.

20 / HK = 25 * X / 9 * X.

HK = 20 * 9 * X / 25 * X.

HK = 180/25 = 7.2 cm.

Answer: The length of the segment HK is 7.2 cm.