Question

The angle of elevation of a cloud from a point hundred metre above the surface of a lake is 30 degree and the angle of depression of the reflection of the cloud in the lake is 60 degree then find the height of the cloud from the lake surface?

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

Answer 2

height is 120 m.. ........