A 1.8 m person stands at a distance of 6 m from a 3.6 m high lamppost. Find the length of the person’s shadow.

Let the segment AK = X m, then the segment AD = (X + 6) m.

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 ACD and ABK are similar in acute angle.

CD / BK = AD / AK.

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

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

3.6 * X – 1.8 * X = 10.8.

1.8 * X = 10.8.

X = 10.8 / 1.8.

X = AK = 6.

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