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A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.
Correct answer is '145.5-145.6'. Can you explain this answer?
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A transmission tower of height 14m was erected to top of a building. A...
In ΔPRS
In ΔPQS
V = Dtan6°
Dtan9° – Dtan6° = 14
D(tan9° – tan6°) = 14
D = 262.76 m
V = 262.76 tan6°
V = 27.62 m
R.L of top of the tower = (R.L)B.M + Staff reading on BM + V + 14
R.L.Q = 102.5 + 1.425 + 27.62 + 14
R.L.Q = 145.545 m
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A transmission tower of height 14m was erected to top of a building. A...
Degrees and 18 degrees respectively. To find the height of the building, we can use the concept of similar triangles.
Let's assume the height of the building is "h" meters.
In the given problem, we have two right-angled triangles: one formed by the theodolite, transmission tower, and the top of the building, and the other formed by the theodolite, transmission tower, and the bottom of the building.
Let's consider the triangle formed by the theodolite, transmission tower, and the top of the building.
In this triangle, the vertical angle at the theodolite is 9 degrees, and the opposite side is the height of the transmission tower, which is 14m.
Using trigonometry, we can write:
tan(9 degrees) = opposite/adjacent
tan(9 degrees) = 14/h
Now, let's consider the triangle formed by the theodolite, transmission tower, and the bottom of the building.
In this triangle, the vertical angle at the theodolite is 18 degrees, and the opposite side is the height of the transmission tower, which is 14m. The adjacent side is the height of the building, which is "h" meters.
Using trigonometry, we can write:
tan(18 degrees) = opposite/adjacent
tan(18 degrees) = 14/h
Now, we have two equations:
tan(9 degrees) = 14/h
tan(18 degrees) = 14/h
Dividing these two equations, we get:
(tan(9 degrees))/(tan(18 degrees)) = (14/h)/(14/h)
tan(9 degrees)/tan(18 degrees) = 1
Using the trigonometric identity: tan(2θ) = 2tan(θ)/(1-tan^2(θ)), we can rewrite the equation as:
tan(2*9 degrees) = 1
tan(18 degrees) = 1
Therefore, the equation is satisfied.
Hence, the height of the building is h = 14 meters.
Let's assume the height of the building is "h" meters.
In the given problem, we have two right-angled triangles: one formed by the theodolite, transmission tower, and the top of the building, and the other formed by the theodolite, transmission tower, and the bottom of the building.
Let's consider the triangle formed by the theodolite, transmission tower, and the top of the building.
In this triangle, the vertical angle at the theodolite is 9 degrees, and the opposite side is the height of the transmission tower, which is 14m.
Using trigonometry, we can write:
tan(9 degrees) = opposite/adjacent
tan(9 degrees) = 14/h
Now, let's consider the triangle formed by the theodolite, transmission tower, and the bottom of the building.
In this triangle, the vertical angle at the theodolite is 18 degrees, and the opposite side is the height of the transmission tower, which is 14m. The adjacent side is the height of the building, which is "h" meters.
Using trigonometry, we can write:
tan(18 degrees) = opposite/adjacent
tan(18 degrees) = 14/h
Now, we have two equations:
tan(9 degrees) = 14/h
tan(18 degrees) = 14/h
Dividing these two equations, we get:
(tan(9 degrees))/(tan(18 degrees)) = (14/h)/(14/h)
tan(9 degrees)/tan(18 degrees) = 1
Using the trigonometric identity: tan(2θ) = 2tan(θ)/(1-tan^2(θ)), we can rewrite the equation as:
tan(2*9 degrees) = 1
tan(18 degrees) = 1
Therefore, the equation is satisfied.
Hence, the height of the building is h = 14 meters.
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A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. Can you explain this answer?
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A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. 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 transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. 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 transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. Can you explain this answer?.
A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. 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 transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. 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 transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. Can you explain this answer?.
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A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. Can you explain this answer?, a detailed solution for A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. Can you explain this answer? has been provided alongside types of A transmission tower of height 14m was erected to top of a building. A theodolite is used to measure vertical angle to top and bottom of the tower and were measured as 9° and 6° respectively. Calculate the Reduced level (metres) of the top of the transmission tower if the staff reading of 1.425m was taken from the same point on a Benchmark of R.L 102.5m. Neglect curvature and refraction correction.Correct answer is '145.5-145.6'. Can you explain this answer? theory, EduRev gives you an
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