A man is observing from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 60 m from the tower. After 5 second, the angle of depression becomes 30°, Find the speed of the boat, assuming that it is running in still water.

Let us draw the figure from the given question.
Let AB = h meter be the height of the tower; C and D are the two points on the ground such that BC = 60 m; ∠ACB = 45° and ∠ADB = 30°
Now from right triangle ABC,
tan 45° = h/60
⇒ 1 = h/60
∴ h = 60 m;
Again from right triangle ABD;
tan 30° = h/(x + 60)
⇒ 1/√3 = 60/(x + 60)
⇒ x + 60 = 60√3
∴ x = 60(1.73 - 1) = 43.8 meter
Hence, speed of boat = 43.8/5 m/s = 43.8/5 x 18/5 = 31.5 km/hr.