Question

A $14-\mathrm{foot}$ tree casts an $8-\mathrm{foot}$ shadow. At the same time, a nearby flagpole casts a $10-\mathrm{foot}$ shadow. Which of the following represents the height of the flagpole to the nearest tenth of a foot?

Answer 1

Step 1: Find the ratio of the tree.

• Let $x-\mathrm{foot}$ be the height of the flagpole.
• A $14-\mathrm{foot}$ tree casts an $8-\mathrm{foot}$ shadow.

$\frac{\mathrm{height}\mathrm{of}\mathrm{object}}{\mathrm{length}\mathrm{of}\mathrm{shadow}}=\frac{14}{8}$

Step 2: Find the ratio of the flagpole.

A $x-\mathrm{foot}$ flagpole casts a $10-\mathrm{foot}$ shadow.

$\frac{\mathrm{height}\mathrm{of}\mathrm{object}}{\mathrm{length}\mathrm{of}\mathrm{shadow}}=\frac{x}{10}$

These two things happens in same time.

Step 3: Find the value of $x$.

Equate both the ratio to find the height of the flagpole:

$\begin{array}{rcl}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{tree}& =& \mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{flagpole}\\ & \Rightarrow & \frac{14}{8}=\frac{\mathrm{x}}{10}\\ & \Rightarrow & 8\mathrm{x}=\left(10\right)\left(14\right)\\ & \Rightarrow & 8\mathrm{x}=140\\ & \Rightarrow & \mathrm{x}=\frac{140}{8}\\ \therefore \mathrm{x}& =& 17.5\mathrm{foot}\end{array}$

Therefore, the height of the flagpole will be $\mathbf{17}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{foot}$.