Home
Class 10
MATHS
The angle of elevation of a cloud from a...

The angle of elevation of a cloud from a point 'h' metres above a lake is `alpha` and the angle of deprssion of its reflection in the lake is `beta`. Pover that the distance of the cloud from the point of observation is `(2hsecalpha)/(tanbeta-tanalpha)`.

Text Solution

AI Generated Solution

To solve the problem, we need to establish the relationship between the angles of elevation and depression, and the distances involved. Let's break it down step by step. ### Step 1: Understand the Setup We have a lake, and a point \( A \) that is \( h \) meters above the lake. The cloud is at point \( B \) and its reflection in the lake is at point \( C \). The angle of elevation from point \( A \) to the cloud \( B \) is \( \alpha \), and the angle of depression from point \( A \) to the reflection \( C \) is \( \beta \). ### Step 2: Define the Distances Let: - \( AB = l \) (the distance from point \( A \) to the cloud \( B \)) ...
Promotional Banner

Topper's Solved these Questions

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|32 Videos
  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (short Answer Questions)|5 Videos
  • REAL NUMBERS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|5 Videos
  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|4 Videos

Similar Questions

Explore conceptually related problems

The angle of elevation of a cloud from a point h mt. above is theta^@ and the angle of depression of its reflection in the lake is phi . Then, the height is

The angle of elevation of a cloud from a point h metre above a lake is theta .The angle depression of its reflection in the lake is 45^@ The height of the cloud is

If the angle of elevation of a cloud from a point h metres above a lake is alpha and the angle of depression of its reflection in the lake is beta , prove that the height of the cloud is (h(tanbeta+t a nalpha))/(tanbeta-t a nalpha)

If the angle of elevation of a cloud from a point h metres above a lake is alpha and the angle of depression of its reflection in the take is beta , prove that the height of the cloud is (h(tanbeta+t a nalpha))/(tanbeta-t a nalpha)

The angle of elevation of a cloud from a point 250 m above a lake is 15^(@) and angle of depression of its reflection in lake is 45^(@) . The height of the cloud is

The angle of elevation of a cloud from a point 60 m above a lake is 30o and the angle of depression of the reflection of cloud in the lake is 60o . Find the height of the cloud.

The angle of elevation of a cloud from a point 60m above a lake is 30^@ and the angle of depression of the reflection of cloud in the lake is 60^@ . Find the height of the cloud.

The angle of elevation of a stationary cloud from a point 25 m above a lake is 30^(@) and the angle of depression of its reflection in the lake is 60^(@) . What is the height of the cloud above that lake-level ?

The angle of elevation of a cloud from a point h metres above the surface of a lake is theta and the angle of depression of its reflection in the lake is phi . Prove that the the height of the cloud above the lake surface is : h ( ( tan phi + tan theta)/( tan phi - tan theta) )

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 .