Question

A 6ft tall person is standing 24ft away from a street light that is 15ft tall. How long is her shadow?

Answer 1

I got `16"ft"`

Explanation:

Consider the diagram:

and the two triangle formed by the lamppost and the man.

We use trigonometry to write:
`h/x=tan(alpha)`
and
`H/(y+x)=tan(alpha)`
let us equate the `tan(alpha)` and write:
`h/x=H/(y+x)`
with numbers:
`6/x=15/(24+x)`
rearrange:
`6(24+x)=15x`
`15x-6x=144`
`9x=144`
`x=144/9=16"ft"`