A 1.8 m tall man stands at a distance of 6 m from the pole on which the lantern hangs at a height

A 1.8 m tall man stands at a distance of 6 m from the pole on which the lantern hangs at a height of 3.6 m. Find the length of the man’s shadow.

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

Both triangles have a common angle A, and both triangles are right-angled, since CD and BK are parallel to AD, then the right-angled triangles ACD and ABK are similar in the first sign of similarity – in an acute angle.

Determine the length of the segment AD.

Let the length of the segment AK = X meters, then the segment AD = X + 6 meters.

Then CD / BK = AD / AK.

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

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

1.8 * X = 10.8.

X = AK = 6 m.

Answer: The length of a person’s shadow is 6 meters.