Triangulation of cell towers

Question

A Satellite sends a signal to cell towers A and B in 2 city's and make an angel of elevation 88 degrees with tower A and an angel of 86 degrees with tower B the satellite is 18000 miles for tower B what is the approximate distance between the 2 city's?   

Answer 1

First make a sketch of two right triangles. One for city A and one for city B with the satellite at the top. The angles for city A will be 88,90 and 2 degrees, and the angles for city B will be 86,90 and 4 degrees.

 

Create an equation to find the bottom leg of city B triangle, it will look like this:

sin(86)=x/18000 solve for x and you get 17,956.15.

Next use the Pythagorean Theorem to get the height of your triangle and you get 1,255.617 (this is slo the height of your A triangle.

 

Set up an equation to find the bottom leg of your A triangle. It will look like this:

tan(88)=x/1255.617 solve for x and you get 35,956.153

 

Add your two lengths together  17,956.15 + 35,956.153 = 53,912.303 miles

 

However, this is assuming the earth is flat.