A person stands at a distance of 3m from a lamppost 3.4m high casts a 3m long shadow. Find the height of the person.

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.

AD = AK + KD = 3 + 3 = 6 meters.

Then CD / BK = AD / AK.

3.4 / ВK = 6/3.

6 * ВK = 3.4 * 3.

6 * ВK = 10.2.

ВK = 1.7 m.

Answer: Human height is 1.7 meters.