Question

The angle of elevation of a cloud from a point10 m above the surface of lake is 30 degree and the angle of depression of the reflection of cloud in the lake is 60 degree find the height of cloud

Answer 1

Answer:

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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