To find the equivalent zenith angle in the reverse mode, we need to understand that a total station measures the zenith angle, which typically ranges from \(0^\circ\) to \(180^\circ\) on either side of the vertical direction (which is often the upward direction). In direct mode, an angle is measured from this upward vertical direction down to the object. Conversely, the reverse mode measures complementarily on the opposite side of this vertical direction.
The relationship between the zenith angles in direct and reverse modes is given by:
\text{Reverse Zenith Angle} = 360^\circ - \text{Direct Zenith Angle}
Given the direct mode zenith angle, \(84^\circ 13' 56"\), we can calculate the reverse mode zenith angle by subtracting this value from \(360^\circ\).
Step-by-Step Calculation:
- Start with \(360^\circ 00' 00"\).
- Subtract the given angle \(84^\circ 13' 56"\) from \(360^\circ\):
| Reverse Angle = | 360° | 00′ | 00″ |
| – | 84° | 13′ | 56″ |
| --- | -- | -- | |
| Result = | 275° | 46′ | 04″ |
Therefore, the equivalent zenith angle in the reverse mode is \(275^\circ 46' 04"\).
Conclusion:
Among the given options,
$275°46′04″$
is the correct zenith angle in reverse mode when the direct mode measurement is $84°13′56″$. Thus, the correct answer is:
$275°46′04″$
Important Questions from Theodolite
- Which of the following errors is/are eliminated by taking both left and right face observations in a theodolite?
- "Transit the telescope" of a theodolite involves
- Choose the CORRECT statement(s).
- Face Left and Face Right observations using a vernier theodolite will eliminate
- An angle of $90^\circ$ is to be laid out with a theodolite having a least count of $30''$. The angle was measured by repetition method and was found to be $90^\circ 00' 25''$. The offset value at a distance of 300 m from the theodolite to set-out the correct angle is _______ m. (Rounded off to 3 decimal places).
