Question

The angle of elevation of a cloud from a point 60m above the surface of the water of a lake is 30 and the angle of depression of its shadow from the same point in water of the lake is 60. Find the height of the cloud from the surface

Answer 1

Answer:

The height of the cloud is 120m

Step-by-step explanation:

From the attached diagram

BC if the height of the cloud

Given:

CD = 60 (opposite sites of ADCE are equal)

Applying Pythagoras rule to calculate AD

Tan60 = CD/AD

AD = CD X Tan60

= 60 X 1.732 = 103.92m

Using Pythagoras rule to find BD

Tan30 = BD/AD

BD = AD X Tan30

= 103.92 X 0.5773

= 59.993

BC = BD + CD

= 59.993 + 60

= 119.993

BC ~ 120m

The height of the cloud is approximately 120m