The back sight at a station A is 0.865 m and the height of instrument is 561.365 m. The reduced level at A is (in m):
Correct Answer: A. 560.500 m
📚 Detailed Explanation: RL of A = HI − BS = 560.500 m
Why A (560.500) is correct: The Height of Instrument (HI) formula is HI = RL(station) + BS. We are given HI and BS; rearranging gives RL = HI − BS.
Formula: HI = RL + BS
Rearranged: RL = HI – BS
Rearranged: RL = HI – BS
Given: HI = 561.365 m, BS = 0.865 m
RL of A = 561.365 – 0.865 = 560.500 m
Why Other Options Are Wrong
| Option | Value | What Calculation Gives This? |
|---|---|---|
| B. 558.705 | 558.705 | 561.365 − 2.66 — wrong operand |
| C. 559.260 | 559.260 | 561.365 − 2.105 — wrong value used |
| A. 560.500 | 560.500 | 561.365 − 0.865 = 560.500 — CORRECT |
| D. 560.550 | 560.550 | Close but not correct; result of arithmetic slip |
- RL = HI − BS = 561.365 − 0.865 = 560.500 m.
- The BS is always the staff reading on a station of known RL; HI = RL + BS.
- To find RL from HI: RL = HI − BS (reverse the formula).