Class 10 Exam > Class 10 Questions > An observer 1.5 m tall is 28.5 m away from a ...
Start Learning for Free
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is
- a)10 m
- b)40 m
- c)30 m
- d)20 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
An observer 1.5 m tall is 28.5 m away from a tower. The angle of eleva...
To solve for the height of the tower, we use the tangent function. The angle of elevation is 45°, and the horizontal distance from the observer to the tower is 28.5 m.
Let the height of the tower be h. The observer's eye level is 1.5 m, so the difference in height between the top of the tower and the observer's eyes is h−1.5h.
Most Upvoted Answer
An observer 1.5 m tall is 28.5 m away from a tower. The angle of eleva...
Understanding the Scenario
To solve the problem, we need to visualize the situation involving the observer and the tower. The observer is standing 28.5 m away from the base of the tower, and his height is 1.5 m. The angle of elevation to the top of the tower is 45 degrees.
Key Concepts
- Angle of Elevation: It is the angle formed by the line of sight of an observer looking up at an object.
- Right Triangle: The observer, the tower, and the ground form a right triangle where:
- The height of the tower is the opposite side.
- The distance from the observer to the tower is the adjacent side.
Calculating the Height of the Tower
1. Right Triangle Properties:
- The height from the observer's eyes to the top of the tower can be calculated using the tangent function since the angle of elevation is 45 degrees.
- For an angle of 45 degrees, the tangent of the angle is equal to 1 (tan(45) = 1).
2. Using the Distance:
- The distance from the observer to the tower is 28.5 m. Therefore, we have:
- Height from observer's eyes to tower top = tan(45 degrees) * distance
- This gives us: Height = 1 * 28.5 m = 28.5 m.
3. Total Height of the Tower:
- Since the observer's height is 1.5 m, the total height of the tower is:
- Total Height = Height from eyes to tower top + Height of observer
- Total Height = 28.5 m + 1.5 m = 30 m.
Conclusion
Thus, the height of the tower is 30 m, which corresponds to option C.
To solve the problem, we need to visualize the situation involving the observer and the tower. The observer is standing 28.5 m away from the base of the tower, and his height is 1.5 m. The angle of elevation to the top of the tower is 45 degrees.
Key Concepts
- Angle of Elevation: It is the angle formed by the line of sight of an observer looking up at an object.
- Right Triangle: The observer, the tower, and the ground form a right triangle where:
- The height of the tower is the opposite side.
- The distance from the observer to the tower is the adjacent side.
Calculating the Height of the Tower
1. Right Triangle Properties:
- The height from the observer's eyes to the top of the tower can be calculated using the tangent function since the angle of elevation is 45 degrees.
- For an angle of 45 degrees, the tangent of the angle is equal to 1 (tan(45) = 1).
2. Using the Distance:
- The distance from the observer to the tower is 28.5 m. Therefore, we have:
- Height from observer's eyes to tower top = tan(45 degrees) * distance
- This gives us: Height = 1 * 28.5 m = 28.5 m.
3. Total Height of the Tower:
- Since the observer's height is 1.5 m, the total height of the tower is:
- Total Height = Height from eyes to tower top + Height of observer
- Total Height = 28.5 m + 1.5 m = 30 m.
Conclusion
Thus, the height of the tower is 30 m, which corresponds to option C.
Free Test
FREE
| Start Free Test |
Community Answer
An observer 1.5 m tall is 28.5 m away from a tower. The angle of eleva...
To solve for the height of the tower, we use the tangent function. The angle of elevation is 45°, and the horizontal distance from the observer to the tower is 28.5 m.
Let the height of the tower be h. The observer's eye level is 1.5 m, so the difference in height between the top of the tower and the observer's eyes is h−1.5h.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
Question Description
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer?.
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer?.
Solutions for An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? 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 An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower isa)10 mb)40 mc)30 md)20 mCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
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