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The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is?
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The angle of elevation of the top of a tower standing on a horizontal ...
Solution:
Given:
- Angle of elevation from point A to the top of the tower = alpha
- Angle of elevation from a point d closer to the tower = beta
To find:
- Height of the tower
Let's break down the solution:
Step 1: Setting up the problem
- Let AB be the height of the tower
- Let AC be the distance from point A to the foot of the tower
- Let CD be the distance walked towards the foot of the tower
Step 2: Applying trigonometry
- In triangle ABC, tan(alpha) = AB/AC
- In triangle ACD, tan(beta) = AB/(AC - d)
Step 3: Solving for the height of the tower
- From the above equations, we can write:
AB = AC * tan(alpha) (1)
AB = (AC - d) * tan(beta) (2)
- Equating equations (1) and (2), we get:
AC * tan(alpha) = (AC - d) * tan(beta)
- Solving for AB, we get:
AB = AC(tan(alpha) - tan(beta))/(tan(beta))
Step 4: Calculating the height of the tower
- Substitute the given values of alpha, beta, and d into the equation we derived in step 3 to find the height of the tower.
Conclusion:
- The height of the tower can be calculated using the formula AB = AC(tan(alpha) - tan(beta))/(tan(beta)). By substituting the given values, we can find the height of the tower.
Given:
- Angle of elevation from point A to the top of the tower = alpha
- Angle of elevation from a point d closer to the tower = beta
To find:
- Height of the tower
Let's break down the solution:
Step 1: Setting up the problem
- Let AB be the height of the tower
- Let AC be the distance from point A to the foot of the tower
- Let CD be the distance walked towards the foot of the tower
Step 2: Applying trigonometry
- In triangle ABC, tan(alpha) = AB/AC
- In triangle ACD, tan(beta) = AB/(AC - d)
Step 3: Solving for the height of the tower
- From the above equations, we can write:
AB = AC * tan(alpha) (1)
AB = (AC - d) * tan(beta) (2)
- Equating equations (1) and (2), we get:
AC * tan(alpha) = (AC - d) * tan(beta)
- Solving for AB, we get:
AB = AC(tan(alpha) - tan(beta))/(tan(beta))
Step 4: Calculating the height of the tower
- Substitute the given values of alpha, beta, and d into the equation we derived in step 3 to find the height of the tower.
Conclusion:
- The height of the tower can be calculated using the formula AB = AC(tan(alpha) - tan(beta))/(tan(beta)). By substituting the given values, we can find the height of the tower.
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The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is?
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The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is?.
The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle of elevation of the top of a tower standing on a horizontal plane from a point A is alpha after walking a distance d towards the foot of the tower the angle of elevation is found to be beta the height of a tower is?.
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