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An observer 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer is
- a)30°
- b)45°
- c)60°
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
An observer 1.5m tall is 23.5m away from a tower 25m high. The angle o...
We are given:
- Height of the observer = 1.5 m
- Distance between observer and tower = 23.5 m
- Height of the tower = 25 m
Calculating the height of the tower above the observer's eye level:
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An observer 1.5m tall is 23.5m away from a tower 25m high. The angle o...
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An observer 1.5m tall is 23.5m away from a tower 25m high. The angle o...
We can use trigonometry to solve this problem. Let's draw a diagram:
```
A
/|
/ |
/ | 25m
/ |
/ |
/θ |
/ |
/_______|
23.5m B
Observer Top of tower
```
In this diagram, A represents the top of the tower, B represents the observer, and θ represents the angle of elevation of the top of the tower from the eye of the observer.
We know that AB = 25m (the height of the tower) and OB = 23.5m (the distance from the observer to the tower). We want to find θ.
We can use the tangent function to find θ:
tan θ = opposite / adjacent
In this case, the opposite side is AB (25m) and the adjacent side is OB (23.5m):
tan θ = 25 / 23.5
Using a calculator, we find that:
θ ≈ 52.2°
However, this is the angle of elevation from the ground. Since the observer is 1.5m tall, their eye level is 1.5m above the ground. So we need to subtract the inverse tangent of 1.5/23.5 to find the angle of elevation from the eye of the observer:
θ' = θ - tan^-1(1.5/23.5)
Using a calculator, we find that:
θ' ≈ 30°
Therefore, the angle of elevation of the top of the tower from the eye of the observer is approximately 30 degrees.
```
A
/|
/ |
/ | 25m
/ |
/ |
/θ |
/ |
/_______|
23.5m B
Observer Top of tower
```
In this diagram, A represents the top of the tower, B represents the observer, and θ represents the angle of elevation of the top of the tower from the eye of the observer.
We know that AB = 25m (the height of the tower) and OB = 23.5m (the distance from the observer to the tower). We want to find θ.
We can use the tangent function to find θ:
tan θ = opposite / adjacent
In this case, the opposite side is AB (25m) and the adjacent side is OB (23.5m):
tan θ = 25 / 23.5
Using a calculator, we find that:
θ ≈ 52.2°
However, this is the angle of elevation from the ground. Since the observer is 1.5m tall, their eye level is 1.5m above the ground. So we need to subtract the inverse tangent of 1.5/23.5 to find the angle of elevation from the eye of the observer:
θ' = θ - tan^-1(1.5/23.5)
Using a calculator, we find that:
θ' ≈ 30°
Therefore, the angle of elevation of the top of the tower from the eye of the observer is approximately 30 degrees.
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An observer 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer isa)30°b)45°c)60°d)none of theseCorrect answer is option 'B'. 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 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer isa)30°b)45°c)60°d)none of theseCorrect answer is option 'B'. 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 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer isa)30°b)45°c)60°d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
An observer 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer isa)30°b)45°c)60°d)none of theseCorrect answer is option 'B'. 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 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer isa)30°b)45°c)60°d)none of theseCorrect answer is option 'B'. 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 1.5m tall is 23.5m away from a tower 25m high. The angle of elevation of the top of the tower from the eye of the observer isa)30°b)45°c)60°d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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