Q18. - Geometry

Question

In Exercises 17-20, the latitude of a city is given. Sketch the earth and a circle of latitude through the city. Find the radius of this circle.

 Columbus, Obie; $40°N$

Step-by-Step Solution

Answer

(a)

The final answer is $4902.68$km. 

Step 1. Given information:

 The latitude of a city Columbus, Ohio is $43°N$.    

Step 2. Concept used:

 We use basic geometric and angle concept

Step 3. Applying the concept:

 Sketch of earth:

Now, from the figure, $r=R\cos 43°$, where $R$ is the radius of the earth, and $r$ is a radius of required circle.

$\therefore r=6400\times \cos 43{}^{\circ },$

$\Rightarrow r=4680.66$ km.