Please refer to the picture below:
This is just a problem about similar triangles. So we know that:
ΔADE ~ ΔABC
Because they share common sides then they are similar so:
[tex] \frac{AC}{AE} = \frac{BC}{DE} = \frac{15}{6} = \frac{5}{2} [/tex]
We let CE be x then this would make:
[tex] \frac{20+x}{20} = \frac{5}{2} \\ (20+x)2=5*20 \\ 40+2x=100 \\ 2x=60 \\ x=30[/tex]
Therefore the man should stand 30 feet from the light to cast a shadow of 20ft long.
