Chapter 6.9, Problem 3PPS

To determine

The length of flagpole shadow using the given information.

Answer to Problem 3PPS

Length of flagpole`s shadow is 45 feet at the same time.

Explanation of Solution

Given information: 

A flagpole is 30 feet high and a mail box is 3.5 feet high. The mailbox casts a shadow that is 5.25 feet.

Concept used: The related figure forming two similar triangles can be drawn as:

  

And as in similar triangles, the ratio of corresponding sides are proportional, so

  $\frac{\text{Height of the flagpole}}{\text{Height of mailbox}}=\frac{\text{Length of shadow of pole}}{\text{Length of shadow of mailbox}}$

Calculation:

Based on above proportion, set,

  $\frac{AB}{DE}=\frac{BC}{CE}$

Or, length of shadow of pole,

  $\begin{array}{c}BC=\frac{30\times 5.25}{3.5}\\ =\frac{157.5}{3.5}\\ =45\end{array}$ (on cross multiply)

So, the length of shadow of flagpole is 45 feet.