At a certain time, a lighthouse is south of a ship. Thirty minutes later, the ship bears N40°20'E from the lighthouse. If the ship is sailing east at 20 kilometers per hour,find the distance of the ship from the lighthouse at each time of observation.

Answer 1

I see a right-angled triangle with a horizontal side of 10 km and its opposite angle 40°20'
for original position SL
tan 40°20' = 10/SL
SL = 10/tan40°20' = 11.7776.. km

for final position LS'
sin40°20' = 10/LS'

you finish it, and state in the required accuracy