How to solve a Parallel Sailing Problem in Navigation?

Parallel sailing is a spherical sailing in which a course is either 090°T or 270°T(east or west direction) in a parallel of latitude.

In this case a vessel A is in position as indicated in the diagram, she wish to travel in point B by means of parallel sailing. So the vessel A needs to travel north to reach the latitude of point B and travel East to reach the longitude of point B. In order to solve problems related to parallel sailing, we need to connect an imaginary lines connecting point A and B even though we will travel on northerly and easterly direction along our parallel of latitude if we wish to use parallel sailing technique. In this example problem, our course and distance travelled was given.

First, we can find out how much is our departure. Departure is the distance covered at the parallel of the latitude we wish to travel. Once we get our departure which in this case is easterly direction, we can find out the latitude of point B. 

After we found out the latitude arrived, we can proceed on finding out the longitude of point B which is given by formula Cosine Mlat= Departure/Dlong as stated in the photo. 

Mlat or middle latitude is the latitude situated/lies between the initial latitude and the latitude arrived. After applying all the formula and calculation as stated in the picture, we can finally find the position of point B by means of latitude and longitude coordinates. 

(Example problem taken from..

Thank you.