Related rates shadow question A $5$ meter lamp is casting a shadow on a $1.8$ meter man walking away at $1.2$ meters a second, how fast is the shadow increasing?
I have no idea how to do this, it feels like there is missing information. I know that this is a problem about triangles but there is some weird trick that has to be used since only two heights are known which are both the same part of a triangle.

Let $x$ be the horizontal distance between the lamp and the man and let $s$ be the length of the shadow. Note that $\dfrac{dx}{dt} = 1.2$ and we are asked to find $\dfrac{ds}{dt}$. By similar triangles (draw a diagram), we have:
$$
\dfrac{1.8}{5} = \dfrac{s}{s+x} \iff 1.8s+1.8x=5s \iff 3.2s=1.8x \iff s = \dfrac{9}{16}x
$$
Hence, by taking the derivative of both sides with respect to $t$, we obtain:
$$
\dfrac{ds}{dt} = \dfrac{9}{16}\dfrac{dx}{dt} = \dfrac{9}{16}(1.2) = \dfrac{27}{40} \text{m/s}$$
