Question

A 6-foot tall person stands x feet away from an 18 foot street light. If the person's shadow is S feet long then what is S equal to in terms of x?

Answer 1

Explanation:

The height of the persion is

$h=6ft$

The height of the street light is

$H=18ft$

The distance from the person to the tree is

$=x$

The length of the person's shadow is

$=S$

Concept:

We will use the ratio below

Man's height IS TO Man's shadow AS Tree's height IS TO Tree's shadow

By applying the concept, we will have that

By using the similar ratio below, we will have

$\begin{gathered} \frac{6}{s}=\frac{18}{s+x} \\ cross\text{ multiply, we will have} \\ 18s=6s+6x \\ 18s-6s=6x \\ 12s=6x \\ \frac{12s}{12}=\frac{6x}{12} \\ s=\frac{1}{2}x \end{gathered}$

Hence,

The final answer is

$s=\frac{1}{2}x$