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

hii. it's answer is 120 m


hope it will help u

Answer 2

Answer:

The Height of the cloud is 120 meters.

Step-by-step explanation:

After constructing the figure of the following case we get to know that:

AB = 60 meters

Let us assume that C is the point of cloud.

The Length CF is the Height of cloud from the surface of water.

We can equate it as CF = h m

We consider two triangles Triangle ABC and Triangle BED. They contain right angles.

EF = AB = 60 m (Opposite Sides Of A Rectangle)

Now, we consider Triangle BEC:

Tan B = Opposite / Adjacent side = CE / BE

Tan 30 = CE / BE

Substituting the values in the equation:

1/√3 = h - 60 / BE

By cross multiplying we get:

BE = √3(h - 60) -----------------(Equation 1)

Now, we consider right triangle BED:

Tan B = Opposite /  Adjacent

Tan 60 = ED / BE

Substituting values in the equation:

√3 = h + 60 / BE

Substituting Equation 1 in the place of BE:

√3 = h + 60 / √3(h - 60)

Cross multiplying we get:

√3 * √3(h - 60) = h + 60

Simplifying,

3 (h - 60) = h + 60

3h - 180 = h + 60

3h - h = 60 + 180

2h = 240

h = 240 / 2 = 120 meters

Therefore, the Height of the cloud is 120 meters.