GATE CE 2019 Set 1 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumTrigonometric LevellingLevellingGeomatics Engineering
Geomatics Engineering → Levelling → Trigonometric Levelling
Last updated
Question
A staff is placed on a benchmark (BM) of reduced level (RL) and a theodolite is placed at a horizontal distance of from the BM to measure the vertical angles. The measured vertical angles from the horizontal at the staff readings of and are found to be the same. Taking the height of the instrument as , the RL (in m) of the theodolite station is ________
Correct answer
100 to 100
Solution
Let be the reduced level of the theodolite station and be the height of the instrument axis above the station.
The reduced level of the instrument axis is .
Let be the magnitude of the vertical angle measured to the staff.
Since the vertical angles from the horizontal are the same for two different staff readings at the same distance , one must be an angle of elevation and the other an angle of depression.
For the staff reading (depression):
--- (1)
For the staff reading (elevation):
--- (2)
Adding equations (1) and (2):
Now, .
The reduced level of the instrument axis is .
Let be the magnitude of the vertical angle measured to the staff.
Since the vertical angles from the horizontal are the same for two different staff readings at the same distance , one must be an angle of elevation and the other an angle of depression.
For the staff reading (depression):
--- (1)
For the staff reading (elevation):
--- (2)
Adding equations (1) and (2):
Now, .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Levelling
2026 Set 1 Q20The Whole Circle Bearing (WCB) of line is . The length of is 100 m. The…2026 Set 2 Q26Which one of the following statements is TRUE with respect to levelling survey?2026 Set 1 Q34A 30 m long tape is standardized at 25 C. It was used to measure the length of a line which…2026 Set 2 Q35A tourist visiting a city holds a map prepared at a scale of . The tourist measures the…2026 Set 1 Q35The height of the plane of collimation of a levelling instrument is 100.000 m from a datum. The…