Question

the angle of elevation of a cloud from a point 100 metre above the surface of a lake is 30 degree and the angle of depression of the reflection of a cloud in the lake is 60 degree find the height of the cloud from the lake surface

Answer 1

In triangle ABC,

tan 30° = AB/BC

1/√3 = h/BC

⇒ BC = h√3 ------(1)

Since the cloud in the lake is a reflection, it will have the same distance as the cloud (refer the figure below)

Therefore, BE =  100 +h

In triangle CBE,

tan 60° = BE/BC

√3 = (100 +100 +h)/ BC

√3 = (200 + h )/BC

∴ BC = (200 + h)/√3 -------(2)

From comparing (1) and (2)

h√3 = (200 + h)/√3

h√3 × √3 = 200 + h

3h = 200 +h

3h - h = 200

2h = 200

∴h = 100 m

Now, height of the cloud = h + 100 m

                                          = 100 + 100

                                          = 200m

Answer 2

Answer:

so the height of the cloud is 200m

I hope it will help