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When the slope of the ground is 15° and the measured distance is 150 m, the correction is _________ m. (Answer up to two decimal places)
Correct answer is '5.11'. Can you explain this answer?
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When the slope of the ground is 15° and the measured distance is 150 ...
Understanding the Ground Slope Correction
To find the correction for a measured distance on a slope, we need to consider the angle of the slope and the horizontal distance. The correction can be calculated using trigonometric principles.
Key Concepts
- Slope Angle: The angle of the slope is given as 15°.
- Measured Distance: The measured distance along the slope is 150 m.
- Horizontal Distance: The horizontal distance can be calculated using the cosine of the slope angle.
Calculating the Correction
1. Calculate Horizontal Distance:
- The formula for calculating the horizontal distance (D) from the slope distance (S) is:
- D = S * cos(θ)
- Here, S = 150 m and θ = 15°.
- Using the cosine of 15° (which is approximately 0.9659):
- D = 150 m * 0.9659 ≈ 144.88 m
2. Determine the Correction:
- The correction (C) is the difference between the measured distance and the horizontal distance:
- C = S - D
- Thus:
- C = 150 m - 144.88 m ≈ 5.12 m
3. Final Adjustment:
- Rounding the result to two decimal places gives the correction as 5.11 m.
Conclusion
In summary, when the slope of the ground is 15° and the measured distance is 150 m, the correction needed is approximately 5.11 m. This adjustment accounts for the slope's impact on the true horizontal distance.
To find the correction for a measured distance on a slope, we need to consider the angle of the slope and the horizontal distance. The correction can be calculated using trigonometric principles.
Key Concepts
- Slope Angle: The angle of the slope is given as 15°.
- Measured Distance: The measured distance along the slope is 150 m.
- Horizontal Distance: The horizontal distance can be calculated using the cosine of the slope angle.
Calculating the Correction
1. Calculate Horizontal Distance:
- The formula for calculating the horizontal distance (D) from the slope distance (S) is:
- D = S * cos(θ)
- Here, S = 150 m and θ = 15°.
- Using the cosine of 15° (which is approximately 0.9659):
- D = 150 m * 0.9659 ≈ 144.88 m
2. Determine the Correction:
- The correction (C) is the difference between the measured distance and the horizontal distance:
- C = S - D
- Thus:
- C = 150 m - 144.88 m ≈ 5.12 m
3. Final Adjustment:
- Rounding the result to two decimal places gives the correction as 5.11 m.
Conclusion
In summary, when the slope of the ground is 15° and the measured distance is 150 m, the correction needed is approximately 5.11 m. This adjustment accounts for the slope's impact on the true horizontal distance.
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Community Answer
When the slope of the ground is 15° and the measured distance is 150 ...
Given: l = 150 m and θ = 15o
Correction is
C = 2lsin2θ/2
= 2(150)sin215/2
= 300sin27.5
= 5.11 m
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When the slope of the ground is 15° and the measured distance is 150 m, the correction is _________ m. (Answer up to two decimal places)Correct answer is '5.11'. Can you explain this answer?
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When the slope of the ground is 15° and the measured distance is 150 m, the correction is _________ m. (Answer up to two decimal places)Correct answer is '5.11'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about When the slope of the ground is 15° and the measured distance is 150 m, the correction is _________ m. (Answer up to two decimal places)Correct answer is '5.11'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When the slope of the ground is 15° and the measured distance is 150 m, the correction is _________ m. (Answer up to two decimal places)Correct answer is '5.11'. Can you explain this answer?.
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