From starting position #O# the bearing of current is #345^@# and that of direction of destination is #100^@#. So the angle between the direction of current and the direction of destination is #(360-345+100)^@=115^@#
Again the ship is to cover 700km in 20hr to reach at the destination
So its velocity along the direction of destination #OD# is
#V_d=700/20=35"km/h"#
The velocity of current along OC
is #V_c=5"km/h"#
Le the velocity of ship along OE will be #V_s# and this velocity makes an angle #alpha# with OD.
Considering cosine law for triangle ODE we can write
#V_s^2=V_c^2+V_d^2-2V_cV_dcos115#
#=>V_s^2=5^2+35^2-2*5*35cos115#
#V_s=37.4"km/h"#
Now applying sin law for triangle ODE we get
#V_d/sin115=5/sinalpha#
#=>37.4/sin115=5/sinalpha#
#=>sinalpha=5/37.4xxsin115~~0.12#
#=>alpha~~7^@#
So the bearing of the direction of the ship to be driven is #107^@#
