NO SIGN BOARDS IN THE OCEAN

       Landmarks are called landmarks because they are found on the land. Then, how to navigate in the ocean. Today, we have electronic GPS devices with satellite connections. How seafarers survived in those days? That is why, they built light houses everywhere.   Let us assume that there is a ship standing in the sea and there are two light houses L and M, on the land separated by 14 miles. 

    A sailor in the ship takes the bearing (angle) of the two light houses using a device.  One light house is 30 degrees to the left of straight-on and another 15 degree to the right. 
    See the figure. The angles A and B are calculated as 76 degrees and 60 degrees using the properties of triangle. 

 

    Using trigonometry, 
14 miles = d/tanA +d/tanB 
14= d(cosA/sinA +cosB/sinB) 
14 = d (sin(A+B)/sinAsinB 
d=14(Sin76.sin60/sin (76+60) =16 miles. 
The ship is 16 miles straight from the land.  This method is called triangulation.  It is used in survey, GPS systems etc. 

 
    During night in mid-sea, no landmark is visible.  Sailors had to navigate using moon and stars. Say H is the angle between horizon and the moon.  Then the ship is at a distance 60*(90-H) nautical miles from the place where the moon is straight overhead. 
     Astronomers published almanacs listing the positions of moon and stars to help navigators. 
 

  
    By looking at the crescent moon, you can find the direction north or south.  From the tip of its horn on top (pointed end), draw a line to its second horn in the bottom. Extend the line, till it touches the horizon. That point is North, if you are in the southern hemisphere of earth and vice versa for others. This method is mostly correct and not perfectly correct. 
    Seafarers explored, invaded, conquered, traded using this technique before the advent of sophisticated electronic devices. Salute the man's endurance.