If the angle of elevation of a cloud from a point which is 25 m above a lake be 30° and the angle of depression of reflection of the cloud in the lake from be 60°, then the height of the cloud (in meters) from the surface of the lake is
- A.50
- B.60
- C.45
- D.42
Show answer and solution
Correct option: A
Solution
Let the cloud be at height h above the lake. Point P is 25 m above the lake.
From P, the cloud is at elevation 30°, so if horizontal distance is d:
tan 30° = (h - 25)/d → d = (h - 25)√3
The reflection of the cloud is at depth h below the lake surface, so it is (h + 25) below P.
Angle of depression to reflection is 60°:
tan 60° = (h + 25)/d → d = (h + 25)/√3
Setting equal: (h - 25)√3 = (h + 25)/√3
3(h - 25) = h + 25
3h - 75 = h + 25
2h = 100
h = 50 m
From P, the cloud is at elevation 30°, so if horizontal distance is d:
tan 30° = (h - 25)/d → d = (h - 25)√3
The reflection of the cloud is at depth h below the lake surface, so it is (h + 25) below P.
Angle of depression to reflection is 60°:
tan 60° = (h + 25)/d → d = (h + 25)/√3
Setting equal: (h - 25)√3 = (h + 25)/√3
3(h - 25) = h + 25
3h - 75 = h + 25
2h = 100
h = 50 m
[JEE Main 2019 · 12 Jan · Shift II]