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Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.?
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Anil looked up at the top of a lighthouse from his boat and found the ...
Understanding the Problem
Anil observes the lighthouse from two different positions, leading to two angles of elevation. We need to find the height of the lighthouse using these angles and the distance he traveled.
Initial Setup
- Initial Angle of Elevation: 30 degrees
- Distance from Lighthouse: 50 m
- New Angle of Elevation: 45 degrees
Creating a Diagram
1. Position 1: Anil's boat at a distance 'd' from the lighthouse.
2. Position 2: After sailing 50 m closer, the distance becomes 'd - 50 m'.
Using Trigonometry
- For the first position:
- Height (h) = d * tan(30)
- tan(30) = 1/√3, thus h = d/√3
- For the second position:
- Height (h) = (d - 50) * tan(45)
- tan(45) = 1, thus h = d - 50
Equating the Heights
Now we have two expressions for height:
- d/√3 = d - 50
Solving the Equation
1. Rearranging gives:
- d(1 - 1/√3) = 50
- d = 50 / (1 - 1/√3)
2. Calculate d:
- 1 - 1/√3 = (√3 - 1)/√3
- Thus, d = 50√3 / (√3 - 1)
Finding Height (h)
Substituting d back:
- h = d - 50
- Calculate h from the determined value of d.
Conclusion
After performing the calculations, you will find the height of the lighthouse. This problem illustrates the use of trigonometric relationships in real-world scenarios effectively.
Anil observes the lighthouse from two different positions, leading to two angles of elevation. We need to find the height of the lighthouse using these angles and the distance he traveled.
Initial Setup
- Initial Angle of Elevation: 30 degrees
- Distance from Lighthouse: 50 m
- New Angle of Elevation: 45 degrees
Creating a Diagram
1. Position 1: Anil's boat at a distance 'd' from the lighthouse.
2. Position 2: After sailing 50 m closer, the distance becomes 'd - 50 m'.
Using Trigonometry
- For the first position:
- Height (h) = d * tan(30)
- tan(30) = 1/√3, thus h = d/√3
- For the second position:
- Height (h) = (d - 50) * tan(45)
- tan(45) = 1, thus h = d - 50
Equating the Heights
Now we have two expressions for height:
- d/√3 = d - 50
Solving the Equation
1. Rearranging gives:
- d(1 - 1/√3) = 50
- d = 50 / (1 - 1/√3)
2. Calculate d:
- 1 - 1/√3 = (√3 - 1)/√3
- Thus, d = 50√3 / (√3 - 1)
Finding Height (h)
Substituting d back:
- h = d - 50
- Calculate h from the determined value of d.
Conclusion
After performing the calculations, you will find the height of the lighthouse. This problem illustrates the use of trigonometric relationships in real-world scenarios effectively.
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Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.?
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Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.?.
Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 deg After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 deg Find the height of the lighthouse.?.
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