Question

A man is walking away from a lamppost with a light source 6 m above the ground. The man is 2 m tall. How long is the man’s shadow when he is 10 m from the lamppost? [Hint: Use similar triangles]

Short answer

The man’s shadow is 5 m.

Step-by-step solution

Step-1. Pair of similar triangles.

$Ratioofbasetobase=Ratioofheighttoheight$

Step-2. Setup the model.

Given that the man is 2 m tall and the light source is 6 m above the ground.

We need to find the man’s shadow when he is 10 m from the lamppost.

Let the man’s shadow is x m.

Thus, the required equation is:

$\begin{array}{l}Ratioofbasetobase=Ratioofheighttoheight\\ \frac{x}{10+x}=\frac{2}{6}\end{array}$

Step-3. Solve for x.

$\begin{array}{l}\frac{x}{10+x}=\frac{1}{3}\\ 3x=10+x\\ 3x-x=10\\ x=\frac{10}{2}\\ x=5\end{array}$

The man’s shadow is 5 m.