Question

the captain of a ship views the top of a lighthouse at an angle of 60degree with the horizontal at an elevation of of 6 meters above sea level.five minutes later,the same captain of the ship views the top of the same lighthouse at an angle of 30degree with the horizontal.determine the speed of the ship if the lighthouse is known to be 50 meters above sea level.

Answer 1

first, we need to find the distance between the ship and the light house:


when 60degree:
\[\tan 60^{o} = 50m/S _{1}\]
\[\S_{1} =50m/\tan 60^{o}=28.8675m\]

when 30 degree:
\[\tan 30^{o}=50m/\S_{2}\]
\[\S_{2}=50m/\tan30^{o}=86.603m\]

total distance traveled = 86.603m-28.867m=57.7355m
5 minute = 5 x 60s = 300s

speed=57.7355m/300s=0.192m/s

i think that is the answer.