If the declination at a place is `10^@` west of north, in which direction should a boat be steered so that it reaches a place (i) due east (ii) due west?

Explanation

Here, GN stands for geographic north, GS for geographic south, GE for geographic east and GW for geographic west. MN stands for magnetic north, MS for magnetic south, MW for magnetic west and ME for magnetic east. As we know that the magnet points towards MN. It is given that declination of the place is `10^@` west of geographic north. This implies that the angle between MN and GN is `= 10^@` with MN declined towards west.
(i) Now, the boat has to reach a place due east i.e. along OR, so it should be steered at an angle of ` theta = + 90^@ = 10^@ + 90^@ = 100^@` with the direction of compass needle (which is always along MN-MS).
(ii) In case the boat has to reach a place due west i.e. along OS, it should be steered at angle of `90^@ - theta = 90^@ - 10^@= 80^@` with the direction of compass needle.