Question

(b) From the top of a cliff the angle of depression to a boat 200 m far away from The cliff is found to be 30°. Find the height of the cliff.

Answer 1

answer

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