Chapter 9.5, Problem 44PS

Solution

To estimate the distance between the Empire State Building and the statue of Liberty.

The distance between the Empire State Building and the statue of Liberty is $6.2\text{ miles}\text{.}$

Given:

It is given that the Chrysler Building and the Empire State Building are about $0.6\text{ miles}$ apart and that the Chrysler Building and the Statue of Liberty are about $5.7\text{ miles}$ apart.

And the angle turned to look at the statue of liberty from the Chrysler Building is ${145}^{°}.$

Calculation:

  

Using the cosine rule, calculating the distance $SE$ as:

  $\begin{array}{l}{\left(SE\right)}^2={\left(CS\right)}^2+{\left(CE\right)}^2-2\left(CS\right)\left(CE\right)\cos E\\ {\left(SE\right)}^2={\left(5.7\right)}^2+{\left(0.6\right)}^2-2\left(5.7\right)\left(0.6\right)\cos {145}^{°}\\ {\left(SE\right)}^2=32.49+0.36-6.84\times \left(-0.819\right)\\ {\left(SE\right)}^2=32.85+5.60\\ {\left(SE\right)}^2=38.45\\ SE=\sqrt{38.45}\\ SE=6.2\end{array}$

Hence, the distance between the Empire State Building and the Statue of Liberty is $6.2\text{ miles}\text{.}$