Question

A surveyor observes a zenith angle of \( 93^\circ \, 00' \, 00'' \) during a theodolite survey. The corresponding vertical angle is

• A. \(- 03^\circ \, 00' \, 00'' \)
• B. \(+ 03^\circ \, 00' \, 00'' \)
• C. \(- 87^\circ \, 00' \, 00'' \)
• D. \(+ 87^\circ \, 00' \, 00'' \)

Hint:

The vertical angle is positive when the line of sight is above the horizontal, and negative when it is below the horizontal.

Answer 1

The Correct Option is A

Step 1: The relationship between the zenith angle (\( Z \)) and the vertical angle (\( V \)) is given by the formula: \[ V = 90^\circ - Z \] Step 2: Given that the observed zenith angle is: \[ Z = 93^\circ \, 00' \, 00'' \] Substituting the value into the formula: \[ V = 90^\circ - 93^\circ \, 00' \, 00'' = -3^\circ \, 00' \, 00'' \] Step 3: Since the result is negative, it indicates that the line of sight is below the horizontal plane. Conclusion: The corresponding vertical angle is \( -03^\circ \, 00' \, 00'' \), which matches option (A).