Q20. - 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.

Rio de Jamarion; $23°S$

Step-by-Step Solution

Answer

The final answer is $5891$km. 

Step 1. Given information:

 The latitude of a city Rio de Janerio is $23°S$.    

Step 2. Concept used:

We use basic geometric and angle concept

Step 3. Applying the concept:

Sketch of earth:

Now, from the figure, $r=R\cos 34°$, where $R$is the radius of  the earth, and $r$is a radius of the required circle.

$\therefore r=6400\times \cos 23{}^{\circ },$

$\Rightarrow r=5891$km.