Chapter 12.7, Problem 33SR

To determine

To find the distance between the two landmarks in miles.

Answer to Problem 33SR

The actual distance between the landmarks to the nearest miles is $\text{3270 miles}$ .

Explanation of Solution

Given information:

The units on the grid are approximately equal to $50,000\text{ feet}$ .

The location of two landmarks are $\left(132,428\right)\text{ and }\left(254,105\right)$ .

Formula used:

The following formula is used:

  $\text{d}=\sqrt{{\left({\text{x}}_2-{\text{x}}_1\right)}^2+{\left({\text{y}}_2-{\text{y}}_1\right)}^2}$

Calculation :

The distance between the two landmarks can be calculated by:

  $\begin{array}{l}\text{d}=\sqrt{{\left({\text{x}}_2-{\text{x}}_1\right)}^2+{\left({\text{y}}_2-{\text{y}}_1\right)}^2}\\ \text{d}=\sqrt{{\left(254-132\right)}^2+{\left(105-428\right)}^2}\\ \text{d}=\sqrt{{\left(122\right)}^2+{\left(323\right)}^2}\\ \text{d}=\sqrt{14884+104329}\\ \text{d}=\sqrt{119213}\\ \text{d}=345.27\end{array}$

The actual distance on the land can be calculated by:

  $\begin{array}{l}345.27\times 50000=17263500\text{ feet}\\ \frac{17263500}{5280}\text{miles }\left[\text{Convert feet into miles}\right]\\ 3269.6\text{ miles or 3270 miles}\end{array}$

Hence, the actual distance between the landmarks to the nearest miles is $\text{3270 miles}$ .