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In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in the
- a)N-W quadrant
- b)N-E quadrant
- c)S-E quadrant
- d)S-W quadrant
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a closed traverse, the sum of south latitudes exceeds the sum of no...
The closing line will have south latitude and east departure. Therefore it will lie in S-E quadrant.
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In a closed traverse, the sum of south latitudes exceeds the sum of no...
Closed Traverse and its properties
A closed traverse is a series of connected survey lines that form a closed polygonal shape. It is used to determine the area and perimeter of a piece of land.
Properties of a closed traverse are:
1. The sum of latitudes (north-south distances) is zero.
2. The sum of departures (east-west distances) is zero.
3. The algebraic sum of the latitudes is equal to the algebraic sum of the departures.
4. The area of the traverse can be calculated using the formula:
Area = ½ (sum of products of latitude and departure)
Solution
In the given problem, it is given that:
1. The sum of south latitudes exceeds the sum of north latitudes.
2. The sum of east departures exceeds the sum of west departures.
From the first property of the closed traverse, we know that the sum of latitudes is zero. Therefore, the sum of north latitudes must be negative (as the sum of south latitudes is greater than the sum of north latitudes).
From the second property of the closed traverse, we know that the sum of departures is zero. Therefore, the sum of west departures must be negative (as the sum of east departures is greater than the sum of west departures).
Now, let us assume that the closing line lies in the N-W quadrant. This means that the closing line is oriented towards the northwest direction.
If the closing line is oriented towards the northwest direction, then it will have a negative departure and a negative latitude. This will make the sum of departures and latitudes both negative, which is not possible.
Therefore, the closing line cannot lie in the N-W quadrant.
Similarly, we can prove that the closing line cannot lie in the N-E or S-W quadrants.
Hence, the only option left is the S-E quadrant, where the closing line can lie.
Therefore, the correct answer is option 'C'.
A closed traverse is a series of connected survey lines that form a closed polygonal shape. It is used to determine the area and perimeter of a piece of land.
Properties of a closed traverse are:
1. The sum of latitudes (north-south distances) is zero.
2. The sum of departures (east-west distances) is zero.
3. The algebraic sum of the latitudes is equal to the algebraic sum of the departures.
4. The area of the traverse can be calculated using the formula:
Area = ½ (sum of products of latitude and departure)
Solution
In the given problem, it is given that:
1. The sum of south latitudes exceeds the sum of north latitudes.
2. The sum of east departures exceeds the sum of west departures.
From the first property of the closed traverse, we know that the sum of latitudes is zero. Therefore, the sum of north latitudes must be negative (as the sum of south latitudes is greater than the sum of north latitudes).
From the second property of the closed traverse, we know that the sum of departures is zero. Therefore, the sum of west departures must be negative (as the sum of east departures is greater than the sum of west departures).
Now, let us assume that the closing line lies in the N-W quadrant. This means that the closing line is oriented towards the northwest direction.
If the closing line is oriented towards the northwest direction, then it will have a negative departure and a negative latitude. This will make the sum of departures and latitudes both negative, which is not possible.
Therefore, the closing line cannot lie in the N-W quadrant.
Similarly, we can prove that the closing line cannot lie in the N-E or S-W quadrants.
Hence, the only option left is the S-E quadrant, where the closing line can lie.
Therefore, the correct answer is option 'C'.
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In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. Can you explain this answer?
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In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. 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 In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. 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 In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. Can you explain this answer?.
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In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in thea)N-W quadrantb)N-E quadrantc)S-E quadrantd)S-W quadrantCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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