In the evening, the street section is illuminated only by a lantern located on a 4.8 m high pole.

In the evening, the street section is illuminated only by a lantern located on a 4.8 m high pole. A 160 cm tall boy is at a distance of 5 m from the lamppost. Determine the length of the boy’s shadow.

Н1 = 4.8 m – column height;

H2 = 160 cm = 1.6 m – boy’s height;

These triangles ABC and A1B1C are similar.

If our triangles are similar, then the corresponding sides are proportional.

You need to make a proportion: H1 / H2 = (5 + X) / X, or

4.8 / 1.6 = (5 + X) / X

We solve the proportion:

4.8 * X = (5 + x) * 1.6;

4.8 * X = 5 * 1.6 + 1.6 * X;

4.8 * X = 8 + 1.6 * X;

4.8 * X – 1.6 * X = 8;

3.2 * X = 8;

X = 8 / 3.2;

X = 2.5

Answer: the length of the shadow is 2.5 m.