Q19. - 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.

Sydney, Australia; $35°S$

Step-by-Step Solution

Answer

The final answer is $5305.84$km. 

Step 1. Given information:

 The latitude of a city Sydney, Australia is $34°S$.    

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.

$\therefore r=6400\times \cos 34{}^{\circ },$

$\Rightarrow r=5305.84$km.