Chapter 5.10, Problem 19STP

To determine

To find: The correct option that shows the height of the bell tower.

Answer to Problem 19STP

The correct option is(D).

Explanation of Solution

Given information: The figures of bell tower and a statue casting shadow are shown below:

  

Calculation:

It can be seen that theabove two triangles are similar. So, their corresponding side lengths are proportional.

To find the height of the bell tower in feet, convert the other units to the same basic unit.

It is known that $1\text{in}\text{.}=0.084\text{ft}$ .

The shadow of statue in feet is:

  $\begin{array}{c}1\text{in}\text{.}=0.084\text{ft}\\ 15\times 1\text{in}\text{.}=15\times 0.084\text{ft}\\ =1.26\text{ft}\end{array}$

The shadow of bell tower in feet is:

  $\begin{array}{c}1\text{in}\text{.}=0.084\text{ft}\\ 60\times 1\text{in}\text{.}=60\times 0.084\text{ft}\\ =5.04\text{ft}\end{array}$

The height of bell tower can be calculated as:

  $\begin{array}{c}\frac{\text{4}\text{.5}\text{ft}}{x}=\frac{\text{1}\text{.26}\text{ft}}{\text{5}\text{.04}\text{ft}}\\ x=\frac{\text{5}\text{.04}\text{ft}}{\text{1}\text{.26}\text{ft}}\times \text{4}\text{.5}\text{ft}\\ x=\text{ 18}\text{feet}\end{array}$

The height of the bell toweris $\text{18}\text{feet}$ .

Therefore, the correct option is (D).