Question

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

Answer 1

x is assumed the height and the value of x=60
so the height is 60+60+60=180

Answer 2

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