Class 10 Exam > Class 10 Questions > A window of a house is h metre above the grou...
Start Learning for Free
A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.?
Verified Answer
A window of a house is h metre above the ground. From the window, the ...
height of another house is h(1 + tanα.cotβ)
see the attachment,
Let AE is the window of one house which is h m metre above from the ground . from the window , angle of elevation (α ) and angle of depression ( β ) of the top and bottom of another house of height BD is shown in figure.
now, AE = BC = h
from ∆BCE ,
tanβ = BC/CE = h/CE
CE = h/tanβ
from ∆DEC ,
tanα = DC/CE
from equation (1) CE = h/tanβ = hcotβ, put it here,
tanα = DC/hcotβ
DC = h.tanα.cotβ
now, we can see that height of another house is BD
BD = BC + CD
from equations (1) and (3)
BD = h + h.tanα.cotβ = h(1 + tanα.cotβ)
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
A window of a house is h metre above the ground. From the window, the ...
Understanding the Problem
In this scenario, we analyze a window at height h metres above the ground. The angles of elevation (alpha) and depression (beta) are observed from this window to the top and bottom of an opposite house, respectively.
Visual Representation
- Imagine a vertical line representing the height of the opposite house.
- The window is at a height of h metres.
- From the window, draw angles alpha (upwards) to the top of the house and beta (downwards) to the bottom.
Using Trigonometry
1. Top of the Opposite House:
- The distance from the window to the top of the opposite house can be expressed using the tangent function:
- Height from window to top = (height of opposite house - h) = d * tan(alpha)
2. Bottom of the Opposite House:
- The distance from the window to the bottom can similarly be expressed:
- Height from window to bottom = (h - 0) = d * tan(beta)
Setting up the Equation
- Let the height of the opposite house be H.
- Then, we can write two equations based on the above observations:
- H - h = d * tan(alpha)
- h = d * tan(beta)
Solving for Height
- Rearranging these equations gives us:
- H = h + d * tan(alpha)
- d = h / tan(beta)
- Substituting d into the equation for H:
- H = h + (h / tan(beta)) * tan(alpha)
Final Result
- Simplifying gives:
- H = h(1 + tan(alpha) * tan(beta))
Thus, the height of the opposite house is h(1 + tan(alpha) * tan(beta)) metres.
In this scenario, we analyze a window at height h metres above the ground. The angles of elevation (alpha) and depression (beta) are observed from this window to the top and bottom of an opposite house, respectively.
Visual Representation
- Imagine a vertical line representing the height of the opposite house.
- The window is at a height of h metres.
- From the window, draw angles alpha (upwards) to the top of the house and beta (downwards) to the bottom.
Using Trigonometry
1. Top of the Opposite House:
- The distance from the window to the top of the opposite house can be expressed using the tangent function:
- Height from window to top = (height of opposite house - h) = d * tan(alpha)
2. Bottom of the Opposite House:
- The distance from the window to the bottom can similarly be expressed:
- Height from window to bottom = (h - 0) = d * tan(beta)
Setting up the Equation
- Let the height of the opposite house be H.
- Then, we can write two equations based on the above observations:
- H - h = d * tan(alpha)
- h = d * tan(beta)
Solving for Height
- Rearranging these equations gives us:
- H = h + d * tan(alpha)
- d = h / tan(beta)
- Substituting d into the equation for H:
- H = h + (h / tan(beta)) * tan(alpha)
Final Result
- Simplifying gives:
- H = h(1 + tan(alpha) * tan(beta))
Thus, the height of the opposite house is h(1 + tan(alpha) * tan(beta)) metres.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.?
Question Description
A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.?.
A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.?.
Solutions for A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? defined & explained in the simplest way possible. Besides giving the explanation of
A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.?, a detailed solution for A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? has been provided alongside types of A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? theory, EduRev gives you an
ample number of questions to practice A window of a house is h metre above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be alpha and beta respectively.Prove that the height of the house is h(1 tanalpha tanbeta) metres.? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup