Home
Class 12
MATHS
The angle of elevation of a stationary c...

The angle of elevation of a stationary cloud from a point 2500 feet above a lake is `30^@` and the angle of depression of its reflection in the lake is `45^@`.Find the height of cloud above the lake water surface .

Text Solution

Verified by Experts

In the figure ,observer is at point B and cloud is at point D.

E is the reflection of colud in the lake .
`therefore` FD =FE =H
In triangle BCD ,
`tan 30 ^@ (H- 2500)/(BC)`
`rArr H- 2500 =BC tan 30 ^@`
In triangle BCE,
`tan 45 ^@=(H+2500)/(BC)`
`rArr H+ 2500 = BC tan 45^@`
`therefore (H-2500)/(H+ 2500)=(BC tan 30^@)/(BC tan 45^@)=1/sqrt(3)`
`rArr sqrt(3)(H-2500 )= H+ 2500`
`rArr (sqrt(3)-1)H=2500 (sqrt(3)+1)`
`rArr H=2500 xx (sqrt(3)+1)/(sqrt(3)-1)` feet
Promotional Banner

Topper's Solved these Questions

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Exercises|18 Videos

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Archives|3 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Exercises|22 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

Similar Questions

Explore conceptually related problems

The angle of elevation of a cloud from a point 200 m above a lake is 30^@ and the angle of depression of its reflection in the lake is 45^@ . Find the height of the cloud from the lake.

The angle of elevation of a cloud from a point h metres above a lake is 45^@ and the angle of depression of its reflection in the lake is 60^@ . Which of the following is the height of the cloud?

From a point at a height of 30 metre from the water level of a lake the angle of elevation of an aeroplane is 30^@ and the angle of depression of the shadow of the aeroplane in water of the lake is 60^@ . What is the height of the aeroplane from the water surface of the lake?

The angle of elevation from the bottom of a tower 20 meter a part is 45^@ . Find the height of the tower.

A statue stands on the top of a 2m tall pedestal. From a point on the ground, the angle ofelevation of the top of the statue is 60^(@) and from the same point, the angle of elevation of the top of the pedestal is 45^(@) . Find the height of the statue.

From a point a metres above a lake the angle of elevation of a cloud is alpha and the angle of depression of its reflection is beta . Prove tha the height of the cloud is (a sin(alpha + beta))/(sin(beta-alpha)) metres.

From the bottom of a 'tila' the angle of elevation of its unreachable top is 45^@ . After moving 100 metre at an angle of 30^@ along the tila the angle of elevation becomes 60^@ . Find the height of the tila. (sqrt3= 1.732)

If the angle of elevation of the top and Monument when observed from a point on the roof of a building of 16 metre height is 60^@ and the angle of depression of the foot of the Monument, when observed from the same point is 30^@ , calculate the height of the Monument and the distance from Monument to the building.

A house of 15 metres height, stands on one side of a park and from a point on the roof of the house the angle of depression of the foor of chimney of brick kiln of the other side is 30^(@) and the angle of elelvation of the top of the chimney of brick kiln is 60^(@) . Find the height of the chimney and the distance between the brick kiln and the house.

From the top of a building, the angle of elevation of the top of a cell tower is 60^(@) and the angle of depression to its foot is 45^(@) . If distance of the building from the tower is 7m, then find the height ofthe tower.