Question

the angle of elevation of a cloud from a point 60m above a lake is 30 degree and the angle of depression of the reflection of the cloud in the lake is 60 degree find the height of the cloud

Answer 1

Let AO=H
CD=OB=60m
A'B=AB=(60+H)m

In triangke AOD,
tan30'=AO/OD=H/OD

H=OD/√3
OD=√3 H

Now, in triangle A'OD,
tan60'=OA'/OD=(OB+BA')/OD
√3=(60+60+H)/√3 H
    =(120+H)/√3 H
 =>120+H=3H
      2H=120
       H=60m

Thus, height of the cloud above the lake = AB+A'B
                                                                 =(60+60)
                                                                 = 120m

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Answer 2

this is the answer height will be h+60=90