Question

The angle of elevation of a cloud from a point 60m above a lake is 30°and the angle of depression of reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.

Answer 1

let AB be surface of lake and P be a point vertically above a such that AP=60
let C be the position of cloud and D be its reflection on the lake
let height of cloud be H metre.

then BC=BD=H
draw PQ perpendicular CD then angle QPC =30  angle QPD = 60
BQ = AP =60M
CQ=H-60     DQ= H+60

IN TRIANGLE CQP PQ/CQ = COT 30
PQ = H-60 X  ROOT 3

IN DQP PQ/DQ = COT 60    1EQN
PQ = H +60/ROOT 3        2 EQN
 

FROM 1 AND 2 EQN
 
H-60 X ROOT3= H+60/ROOT3

3H-180= H+60
2H = 240
H =120 HENCE HEIGHT OF CLOUD IS 120M

Answer 2

Answer is 120m

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