Question

The multiplying constant and additive constant of a tacheometer are 100 and 2 m respectively. When the line of sight is horizontal and the staff held vertically, the staff readings are 2.780 m and 1.280 m respectively, then the distance between the tacheometer and staff station is

• A. 152 m
• B. 150 m
• C. 76 m
• D. 75 m

Hint:

The basic tacheometry distance formula is $D = Ks + C$.
This applies when the telescope is horizontal.
A common mistake is to forget to add the additive constant ($C$) after multiplying $K$ and $s$.
If the telescope is inclined, more complex formulas involving $\cos^2\theta$ and $\sin\theta\cos\theta$ are used.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to calculate the horizontal distance from a tacheometer to a staff station using the provided stadia readings and instrument constants.

Step 2: Key Formula or Approach:
The formula for calculating the horizontal distance ($D$) in tacheometry when the line of sight is horizontal is:
\[ D = Ks + C \] where:
$K$ = Multiplying constant
$C$ = Additive constant
$s$ = Staff intercept (the difference between the top and bottom stadia hair readings)

Step 3: Detailed Explanation:
First, identify the given values:

• Multiplying constant ($K$) = 100

• Additive constant ($C$) = 2 m

• Top staff reading = 2.780 m

• Bottom staff reading = 1.280 m


Next, calculate the staff intercept ($s$):
\[ s = \text{Top reading} - \text{Bottom reading} \] \[ s = 2.780 \text{ m} - 1.280 \text{ m} = 1.500 \text{ m} \] Now, substitute the values into the distance formula:
\[ D = Ks + C \] \[ D = (100 \times 1.500) + 2 \] \[ D = 150 + 2 \] \[ D = 152 \text{ m} \]

Step 4: Final Answer:
The distance between the tacheometer and the staff station is 152 m.