Chapter 13.1, Problem 2MRE

To determine

To find: The distance of New York from the north pole of the earth.

Answer to Problem 2MRE

The New York is about $3400$ miles from the north pole of the earth.

Explanation of Solution

Given information:

The given latitude of New York is ${40.7}^{o}N$ in the figure as below.

  

Calculation:

Consider the figure.

  

Latitude of a point $p$ shown in the figure of the earth at the right it is measure of $\angle EOP$ .

The radius of the earth is about $4000$ miles.

Thus,

  $r=4000$

  $\theta ={40.7}^o$

  $\begin{array}{l}\theta \text{'}={90}^o-{40.7}^{o}N={49.3}^{o}N\\ \end{array}$

We know that,

  $1^o=\frac{\pi }{180}\text{radians}$

Thus,

  $\begin{array}{c}{49.3}^o=\frac{\pi }{180}\times 49.3^o\\ \Rightarrow 49.3^o=0.8604\text{ radians}\end{array}$

Thus,

  $\begin{array}{c}s=r\theta \\ =\left(4000\right)\left(0.8604\right)\\ =3441.6\\ \approx 3400\end{array}$

  $s=3400$ (rounded to nearest hundreds)

Therefore, the New York is about $3400$ miles from the north pole of the earth.