Question

The angle of elevation of a cloud from a point 20 m above a lake ( point A ) is 30. If the angle of depression of its reflection from point A is 60, then find the distance of cloud from point A.

Answer 1

Answer:

If the vertical height of cloud from level of A is H, then the reflection is seen from A at a depth of H+20 from ground level in the lake.

we have, tan 30 = H/AD = 1/√3 or AD = H√3 ............................(1)

we have , tan60 = FD/AD = (H+40)/AD = √3 or H+40 = AD√3 = 3H .......................(2)

[ we used AD = H√3 in above eqn.(2) using eqn.(1) ]

since, H+40 = 3H, we have H = 20 m

Distance of cloud from A = AC = 2H = 40 m