Finding Radius Of The Parallel Of latitude

The mean radius of the earth is 3440 nautical miles, find the radius of the parallel of latitude of Manila (Lat. 14° 30' N approximately).

Given:

Latitude 14° 30' N

Earth's radius = 3440 nautical miles

What is asked:

Radius of the parallel at latitude 14° 30' N

Solution:

1. We are to solve first for the circumference of the parallel at latitude 14° 30' N before we can solve its radius.

              Circumference = 2πr × Cos Lat
                                        = 2 × 3.1416 × 3440 × Cos 14° 30'
                                        = 20925.74 nm

2. Since we have now the value of the circumference of the earth at Latitude 14° 30' N, we can now 
solve the radius of this parallel of latitude. Cross multiplying the formula of getting the 
circumference we can solve for the radius.
            
            Circumference = 2πr 
                            Radius = Circumference 
                                                     2π         
                            Radius = 20925.74 nm   
                                               2 × 3.1416
                                        =  20925.74 nm   
                                                 6.2832
                                        = 3330.42 nm