Question

If the angle of elevation of a cloud from a point 10 metres above a lake is 30 degree and the angle of depression of its reflection in the lake is 60 degree, find the height of the cloud from the surface of lake

Answer 1

Given:

The angle of elevation of the cloud from a point is 10m above a lake is 30 degrees and the angle of depression of its reflection in the lake is 60 degrees.

To Find:

The height of the cloud from the surface of the lake.

Solution:

Let BC be the surface of the water. D is the point of observation. A is the point of the cloud and A' be the position of the reflection of the cloud in the lake.

The angle of elevation from point D is 30° which is ∠ADO = 30°. and the depression of the reflection of cloud in the lake is 60° which means ∠A'TO = 60°.

Let AO be hm.

CD = OB = 60m

A'B = AB = 60+h ..(i)

Now, In ΔAOD,

tan30° = $\frac{1}{\sqrt{3} }$

           = $\frac{height}{base}$

           = $\frac{AO}{OD}$

           = $\frac{h}{\sqrt{3} }$

        h =  $\frac{OD}{\sqrt{3} }$

     ∴ OD = √3h

Now, In ΔA'OD

tan60° = √3

           = $\frac{OA'}{OD}$

           = $\frac{OB+BA'}{OD}$

Substituting the values,

       √3    = $\frac{60+60+h}{\sqrt{3}h }$

                = $\frac{120+h}{\sqrt{3h} }$

Then using equation(i)

A'B = AB = 60 + h

⇒ 120+h = 3h

⇒ 120 = 2h

⇒ h = 120/2

⇒ h = 60m

Therefore, the height of the cloud from the surface of the water is 60m.

Answer 2

Answer:

h+10=the height from the lake to the cloud

so 10+10=20m