Question

The angle of elevation from a point 60m above the lake to a cloud is 30 an angle of depression to reflection of cloud is 60. Find height of cloud .​

Answer 1

Let AO=H

CD=OB=60m

A'B=AB=(60+H)m

In triangle 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

( ' represents degree sign)

Answer 2

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