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A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.?
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A 30m chain is used to measure a line along a gradient of 1:10 . Later...
Given Information:
- Length of the chain used to measure the line: 30m
- Gradient of the line: 1:10
- Misalignment of the chain during measurement: 0.6m
- Length measured along the slope: 90m
Calculation:
To determine the horizontal distance, we need to take into account the gradient of the line and the misalignment of the chain during measurement.
Step 1: Calculate the vertical distance:
The gradient of the line is given as 1:10, which means that for every 10 units of horizontal distance, there is 1 unit of vertical distance. Therefore, the vertical distance covered along the slope can be calculated as follows:
Vertical distance = (Length measured along the slope / Gradient)
= (90m / 10)
= 9m
Step 2: Correct for misalignment:
Since the chain was misaligned by 0.6m, we need to subtract this misalignment from the vertical distance calculated in step 1 to get the correct vertical distance:
Corrected vertical distance = Vertical distance - Misalignment
= 9m - 0.6m
= 8.4m
Step 3: Calculate the horizontal distance:
To calculate the horizontal distance, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the vertical distance (a) is 8.4m and the horizontal distance (b) is what we need to find. The hypotenuse (c) is the length of the chain used, which is 30m.
Using the Pythagorean theorem, we can solve for the horizontal distance as follows:
c^2 = a^2 + b^2
30^2 = 8.4^2 + b^2
900 = 70.56 + b^2
b^2 = 829.44
b = √829.44
b ≈ 28.79m
Therefore, the horizontal distance is approximately 28.79m.
- Length of the chain used to measure the line: 30m
- Gradient of the line: 1:10
- Misalignment of the chain during measurement: 0.6m
- Length measured along the slope: 90m
Calculation:
To determine the horizontal distance, we need to take into account the gradient of the line and the misalignment of the chain during measurement.
Step 1: Calculate the vertical distance:
The gradient of the line is given as 1:10, which means that for every 10 units of horizontal distance, there is 1 unit of vertical distance. Therefore, the vertical distance covered along the slope can be calculated as follows:
Vertical distance = (Length measured along the slope / Gradient)
= (90m / 10)
= 9m
Step 2: Correct for misalignment:
Since the chain was misaligned by 0.6m, we need to subtract this misalignment from the vertical distance calculated in step 1 to get the correct vertical distance:
Corrected vertical distance = Vertical distance - Misalignment
= 9m - 0.6m
= 8.4m
Step 3: Calculate the horizontal distance:
To calculate the horizontal distance, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the vertical distance (a) is 8.4m and the horizontal distance (b) is what we need to find. The hypotenuse (c) is the length of the chain used, which is 30m.
Using the Pythagorean theorem, we can solve for the horizontal distance as follows:
c^2 = a^2 + b^2
30^2 = 8.4^2 + b^2
900 = 70.56 + b^2
b^2 = 829.44
b = √829.44
b ≈ 28.79m
Therefore, the horizontal distance is approximately 28.79m.
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A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.?
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A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.? 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 A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.?.
A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.? 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 A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 30m chain is used to measure a line along a gradient of 1:10 . Later it was detected that the chain was misaligned by 0.6m while the measurement was made. Determine the horizontal distance if the length measured along the slope was 90m.?.
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