Question

A pine tree casts a shadow of 80 feet next to a 30 foot tall building which casts a 40 feet shadow. How tall is the pine tree?

Short answer

The pine tree is 60 feet long.

Step-by-step solution

Given information

The pine tree casts the shadow 80 feet along with the 30-feet tall building casts the shadow 40 feet.

Find the length of the pine tree

Apply the proportions to find the length of the poll.

• As given, the proportion for the tree and the building with respect to the shadow is the same.
• Hence solve equation (1) to find the value of h that represents the length of the tree.

$\begin{array}{rcl}\frac{h}{80}& =& \frac{30}{40}\\ h& =& \frac{30}{40}\times 80\\ & =& 30\times 2\\ & =& 60feet\end{array}$