Question

1. From the top of cliff 50m high, the angles of depression of two boats which are due north of the observer are 60 and 30 degree. find the distance between the boats.
2. A man in a boat being rowed away from a cliff 15m high, takes two minutes to change the angle of elevation of the top of the cliff from 60 and 45 degree. find the speed of the boat.

Please give the answers fast!!

Answer 1

Let x1 = distance from bottom of cliff to first boat (at 25 degree angle of depression - from horizontal)

x2 = distance from bottom of cliff to second boat (at 20 degree angle of depression - from horizontal)

d = x2 - x1 = distance boats are apart from each other (m)

h = height of cliff from water surface = 200 m

x1 = h/[tan(25o)] = (200 m)/(0.4663) = 428.9 m

x2 = h/[tan(20o)] = (200 m)/(0.3640) = 549.5 m

d = x2 - x1 = 549.5 m - 428.9 m = 120.6 m apart

Hope it helps