29. The angle of elevation of a cloud from a point 60 mabove the surfa

1.	29. The angle of elevation of a cloud from a point 60 mabove the surface of the water of a lake is 30 andthe angle of depression of its shadow in water oflake is 60Â°. Find the height of the cloud from thesurface of water.
Answer» Let AO=HCD=OB=60mA'B=AB=(60+H)m In triangke AOD,tan30'=AO/OD=H/OD H=OD/√3OD=√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

29. The angle of elevation of a cloud from a point 60 mabove the surface of the water of a lake is 30 andthe angle of depression of its shadow in water oflake is 60Â°. Find the height of the cloud from thesurface of water.

Answer»

Let AO=HCD=OB=60mA'B=AB=(60+H)m

In triangke AOD,tan30'=AO/OD=H/OD

H=OD/√3OD=√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