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.
