Question

angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its Shadow from the same point in the water of lake is 60 degree hence find the height of the cloud from the surface of the water

Answer 1

Answer:

Step-by-step explanation:

Let C be the position of cloud and TB its reflection in the lake

Let it be the surface of the lake and B be the point of observation

From the given figure

Angle CBA is equal to 30 degree and Angle d b a is equal to 60 degree

Let x is equal to X then C is equal to X + 60

In triangle abc

Tan 30 degree =AC/AB

1/ROOT 3=x/AB

AB=ROOT3.x

In triangle abt

Tan 60 =AT/AB

Tan 60=AE+TE/AB

root3=x+60+60/root3.x

x+120=3x

3x-x=120

2x=120

x=60

CE=AC+AE

CE=x+60

CE=60+60

,CE=120m.

The height of the cloud from the surface of the lake is 120 m