A man with a height of 1.5 m stands at a distance of 9 steps from the pole on which the lantern hangs.

A man with a height of 1.5 m stands at a distance of 9 steps from the pole on which the lantern hangs. The shadow of a person is equal to three steps. At what height (in meters) is the lantern located?

AB – a person, A1B1 – a lantern, OA – a person’s shadow, AA1 – a distance from a pole to a person.

Triangles AOB and A1OB1 are similar in two angles (<O – common, <A = <A1 = 90). If the triangles are similar, then their respective sides are proportional.

A1B1: AB = OA1: OA; OA1 = 9 + 3 = 12 (w.)

x / 1.5 = 12/3 – the product of the extreme terms of the proportion is equal to the product of the middle terms of the proportion;

3x = 1.5 * 12;

3x = 18;

x = 18: 3;

x = 6 (m).

Answer. 6 meters.