## 284. Math Puzzle $1 / 89$

At an airport, a searchlight is installed on a $40 \mathrm{~m}$ high building. $600 \mathrm{~m}$ away from this building, a $12 \mathrm{~m}$ high flight safety installation blocks the view in one direction.

How long is the horizontally running stretch that cannot be seen at night from the searchlight because it lies in the shadow of the flight safety installation.
According to the ray theorem, for the measurements in m:

$$
40: 12=(600+x): x \quad, \quad 40 x=7200+12 x \quad, \quad x=257.14
$$

![](https://cdn.mathpix.com/cropped/2024_06_06_69be9c4355ed0dc2557cg-92.jpg?height=329&width=585&top_left_y=1069&top_left_x=747)

(Figure not to scale) The air traffic control facility will cast a shadow of approximately $257 \mathrm{~m}$.