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A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite station from tower X is 60m. Observations were taken from the theodolite to the top of tower X and tower Y and were recorded as 350 and 300 respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of the tower Y.____m
(Important - Enter only the numerical value in the answer)
Correct answer is '207.27'. Can you explain this answer?
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A theodolite was setup in between two towers X and Y. The distance bet...
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A theodolite was setup in between two towers X and Y. The distance bet...
The question is asking to find the Reduced Level (R.L.) of the top of tower Y given the setup of a theodolite between two towers X and Y. The distance between the two towers is 180m, and the distance of the theodolite station from tower X is 60m. The observations from the theodolite to the top of tower X and tower Y were recorded as 350 and 300 respectively, with the telescope focused upward for both cases. The R.L. of the top of tower X is given as 180m.
To solve this problem, we can use the principle of trigonometry and the concept of the horizontal line of sight.
1. Determine the height difference between the theodolite station and the top of tower X:
The height difference between the theodolite station and the top of tower X can be calculated using the equation:
Height difference = Observation to tower X - Distance from theodolite station to tower X
Height difference = 350 - 60 = 290m
2. Determine the angle of elevation from the theodolite to the top of tower X:
The angle of elevation can be calculated using the equation:
Angle of elevation = arctan(Height difference / Distance from theodolite station to tower X)
Angle of elevation = arctan(290 / 60) = 78.69 degrees
3. Determine the angle of depression from the theodolite to the top of tower Y:
Since the telescope is focused upward for both observations, the angle of depression from the theodolite to the top of tower Y is the same as the angle of elevation to the top of tower X. Therefore, the angle of depression is also 78.69 degrees.
4. Determine the height difference between the theodolite station and the top of tower Y:
The height difference between the theodolite station and the top of tower Y can be calculated using the equation:
Height difference = Distance from theodolite station to tower Y * tan(Angle of depression)
Height difference = 180 * tan(78.69) = 607.27m
5. Determine the R.L. of the top of tower Y:
The R.L. of the top of tower Y can be calculated by adding the height difference between the theodolite station and the top of tower Y to the R.L. of the top of tower X:
R.L. of top of tower Y = R.L. of top of tower X + Height difference
R.L. of top of tower Y = 180 + 607.27 = 787.27m
Therefore, the R.L. of the top of tower Y is 207.27m.
To solve this problem, we can use the principle of trigonometry and the concept of the horizontal line of sight.
1. Determine the height difference between the theodolite station and the top of tower X:
The height difference between the theodolite station and the top of tower X can be calculated using the equation:
Height difference = Observation to tower X - Distance from theodolite station to tower X
Height difference = 350 - 60 = 290m
2. Determine the angle of elevation from the theodolite to the top of tower X:
The angle of elevation can be calculated using the equation:
Angle of elevation = arctan(Height difference / Distance from theodolite station to tower X)
Angle of elevation = arctan(290 / 60) = 78.69 degrees
3. Determine the angle of depression from the theodolite to the top of tower Y:
Since the telescope is focused upward for both observations, the angle of depression from the theodolite to the top of tower Y is the same as the angle of elevation to the top of tower X. Therefore, the angle of depression is also 78.69 degrees.
4. Determine the height difference between the theodolite station and the top of tower Y:
The height difference between the theodolite station and the top of tower Y can be calculated using the equation:
Height difference = Distance from theodolite station to tower Y * tan(Angle of depression)
Height difference = 180 * tan(78.69) = 607.27m
5. Determine the R.L. of the top of tower Y:
The R.L. of the top of tower Y can be calculated by adding the height difference between the theodolite station and the top of tower Y to the R.L. of the top of tower X:
R.L. of top of tower Y = R.L. of top of tower X + Height difference
R.L. of top of tower Y = 180 + 607.27 = 787.27m
Therefore, the R.L. of the top of tower Y is 207.27m.
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A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. Can you explain this answer?
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A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. 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 A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. 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 A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. Can you explain this answer?.
A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. 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 A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. 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 A theodolite was setup in between two towers X and Y. The distance between the two tower is 180m. The distance of theodolite stationfrom tower X is 60m. Observationswere taken from the theodolite tothe top of tower X and tower Y andwere recorded as 350 and 300respectively, telescope focussed upward for both the cases. The R.L. of the top of the tower X is 180m. Calculate the R.L. of the top of thetower Y.____m(Important - Enter only the numerical value in the answer)Correct answer is '207.27'. Can you explain this answer?.
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