The angle of elevation of a cloud from a point 60 m above the surface

1.	The angle of elevation of a cloud from a point 60 m above the surface of the water of a lakeis 30Â° and the angle of depression of its shadow from the same point in water of lake is 60.Find the height of the cloud from the surface 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

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lakeis 30Â° and the angle of depression of its shadow from the same point in water of lake is 60.Find the height of the cloud from the surface 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