A tree with a height of 1.8 meters grows at a distance of 6 meters from the post on which the lantern weighs

A tree with a height of 1.8 meters grows at a distance of 6 meters from the post on which the lantern weighs at a height of = 3.6 meters. Find the length of the tree.

Let the segment AK = X cm, then the segment AD = AK + DK = X + 6 cm.

Let us prove that triangle ACD is similar to triangle ABK.

Both triangles are straight, since CD and BK are perpendicular to AD, and the angle A is common for the triangles, then the triangles are similar in acute angle.

CD / BK = AD / AK.

3.6 / 1.8 = (X + 6) / X.

3.6 * X = 1.8 * X + 10.8.

1.8 * X = 10.8.

X = AK = 10.8 / 1.8 = 6 m.

Answer: The length of the tree shadow is 6 meters.