Question

A man is watching from the top of a tower, a boat speeding away from
the tower. The angle of depression from the top of the tower to the boat
is 60° when the boat is 80 m from the tower. After 10 seconds, the
angle of depression becomes 30°. What is the speed of the boat?
(Assume that the boat is running in still water).​

Answer 1

Answer:

4m/s or 14.4 km/hr

Step-by-step explanation:

height of the tower =

tan30= h/60

h= 60*tan30=60*(1/√3)=20√3

so height of the tower =20√3 meters

so in the initial position how far this boat from the foot of the tower

that one we need to find so that in 10 sec how far it travelled

so tan60=(20√3)/initial distance

initial distance = 20√3/tan60=(20√3)/√3 =20m

so that means it travelled 60-20 =40m in 10 sec

so speed of the boat = distance /time =40/10=4m/s

so if you want to convert into km/hr multiply with 18/5 so it will gives us 4*18/5=14.4 km/hr