Joe is 1.6m tall. His shadow is 2m long when he stands 3m from the base of a floodlight.

height

1.6 m

2m

3m

What is the height of the floodlight?

2.4 m 2.6 m 4.0 m 4.2 m

Answer: 4m

Procedure

Call x the height of the floodlight.

You can draw two similar right triangles with this ratios:

x / (2 + 3) = 1.6 / 2

This is: the height of the floodlight is to the length of shadow + the distance of Joe from the foodlight, as the height of Joe is to the length his shadow.

Then,

x / 5 = 1.6 / 2 ⇒ x = 5*1.6/2 = 4.