Question

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

Answer 1

Answer:

tan 60=p/b

=rot3x=60

x=60/rot3

sec 60=p/b

2=y/x

2=y/60/rot3

2=rot3*y/60

120=rot3*y

y=120/rot3

y=120*rot3/rot3*rot3

y=120*rot3/3

y=60*rot3

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