Chapter 13.1, Problem 1MRE

To determine

To find: The distance of latitude from the equator.

Answer to Problem 1MRE

The Huston is about $2100$ miles from the equator of the earth.

Explanation of Solution

Given information:

The given latitude of Huston is ${29.8}^{o}N$ 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,

  $r=4000$

  $\theta ={29.8}^{o}N$

We know that,

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

Thus,

  $\begin{array}{c}{29.8}^o=\frac{\pi }{180}\times 29.8\\ \Rightarrow {29.8}^o=0.5201\text{ radians}\end{array}$

Thus,

  $\begin{array}{c}s=r\theta \\ =\left(4000\right)\left(0.5201\right)\\ =2080.4\\ \approx 2100\end{array}$

Therefore, the Huston is about $2100$ miles from the equator of the earth.