Hello, anonymous_maths!
A spotlight is on the ground 20m away from a wall.
A 2m tall person is walking towards the wall at a rate of 1.5m/s.
How fast is the height of the shadow changing when the person is 8m from the wall?
Is the shadow increasing or decreasing in height at this time? Code:

S o
:  *
:  *
:  * P
h  o
:   *
:  2 *
:   *
T ooo L
: x Q 20x :
:     20      :
The light is at $\displaystyle L\!:\;\;TL = 20$
The person is: .$\displaystyle PQ = 2$
His distance from the wall is: .$\displaystyle x \:=\:TQ \quad\Rightarrow\quad QL \:=\:20x$
This distance is decreasing at: .$\displaystyle \frac{dx}{dt} \:=\:\text{}\frac{3}{2}$ m/sec.
The height of his shadow is: .$\displaystyle h = ST.$
From the similar right triangles, we have:
. . $\displaystyle \frac{h}{20} \:=\:\frac{2}{20x} \quad\Rightarrow\quad h \:=\:40(20x)^{1} $
Differentiate with respect to time: .$\displaystyle \frac{dh}{dt} \;=\;\text{}40(2x)^{2}(\text{}1)\frac{dx}{dt} \;=\;\frac{40}{(20x)^2}\frac{dx}{dt} $
When $\displaystyle x = 8\!:\;\;\frac{dh}{dt} \;=\;\frac{40}{12^2}\left(\text{}\frac{3}{2}\right) \;=\;\frac{5}{12}$
The height of the shadow is decreasing at $\displaystyle \tfrac{5}{12}$ meters per second.