Question

the angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 300 and the angle of depression of its shadow from the same point in water of lake is 600 . find the height of the cloud from the surface of water

Answer 1

The height of the cloud from the surface of water is 120 m.

How to calculate the height of the cloud from the surface?

The height of the cloud from the surface of water is calculated by applying the principle of trigonometry ratio.

In the diagram, if we consider triangle ABC;

tan 30 = BC / AB

AB = BC / tan 30

AB = BC √3

Also, if we consider triangle ABF;

tan 60 = BF / AB

tan 60 = ( 60 + EF )/BC √3

based on the diagram; EF = EC

EF = 60 + BC

tan 60 = ( 60 + 60 + BC )/BC √3

√3 = ( 60 + 60 + BC )/BC √3

3BC = 120 + BC

3BC - BC = 120

2BC = 120

BC = 120/2

BC = 60 m

The height of the cloud = 60 m + BC

= 60 m + 60 m

= 120 m