Starting from a benchmark and working towards a proposed building lot you have backsight readings of 1.243m, 1.527m, and 1.836m.  Your foresight readings are 0.857m, 1.351m, and 1.325.  What is the elevation of the proposed building lot if the elevation of the benchmark is 100m'

We will use the leveling technique again to find the elevation of the proposed building lot. The key formula is:

\[
\text{Elevation at point} = \text{Initial Elevation} + \sum(\text{Backsight Readings}) - \sum(\text{Foresight Readings})
\]

Let's break it down step by step:

### Step 1: Known Data
- **Backsight (BS) readings:** 1.243 m, 1.527 m, 1.836 m
- **Foresight (FS) readings:** 0.857 m, 1.351 m, 1.325 m
- **Benchmark Elevation (BM):** 100 m

### Step 2: Sum of Backsight and Foresight Readings
- Sum of backsight readings:
  \[
  \text{Sum of BS} = 1.243 + 1.527 + 1.836 = 4.606 \, \text{m}
  \]

- Sum of foresight readings:
  \[
  \text{Sum of FS} = 0.857 + 1.351 + 1.325 = 3.533 \, \text{m}
  \]

### Step 3: Calculate the Elevation of the Proposed Building Lot
Now, use the formula:
\[
\text{Elevation of proposed lot} = \text{BM Elevation} + \text{Sum of BS} - \text{Sum of FS}
\]

Substitute the known values:
\[
\text{Elevation of proposed lot} = 100 + 4.606 - 3.533 = 101.073 \, \text{m}
\]

### Final Answer:
The elevation of the proposed building lot is **101.073 meters**.

Would you like further clarification on any part of this calculation?

Here are five related questions you might consider:
1. What happens to the elevation if the foresight readings increase?
2. How would the calculation change if the benchmark elevation were lower?
3. How are backsight and foresight readings used in calculating slope?
4. What are common sources of error in backsight/foresight measurements?
5. How do you adjust if there are intermediate points between the benchmark and the proposed lot?

**Tip:** When recording backsight and foresight readings in fieldwork, always ensure readings are accurate by taking measurements multiple times to minimize errors.

Starting from a benchmark and working towards a proposed building lot, you have backsight readings of 1.243m, 1.527m, and 1.836m. Your foresight readings are 0.857m, 1.351m, and 1.325m. What is the elevation of the proposed building lot if the elevation of the benchmark is 100m?

Learn how to calculate the elevation of a proposed building lot using backsight and foresight readings. This step-by-step solution starts with a benchmark elevation of 100m and uses leveling techniques to find the final elevation as 101.073m. Ideal for students in Grades 10-12 or anyone studying surveying or construction mathematics.

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