Short Answer:

To measure angles in triangulation, surveyors use precision instruments like a theodolite or total station. The instrument is placed at a triangle’s vertex, and the horizontal angles between two known points are measured. These angles, along with one known baseline length, are used to calculate the unknown sides and positions.

Accurate angle measurement is the key step in triangulation. Surveyors follow proper procedures to set up the instrument, level it, and take repeated readings to avoid errors. The measured angles help form the basis for calculating distances using trigonometry.

Detailed Explanation:

Measuring angles in triangulation

In triangulation surveying, measuring angles accurately is the most important step in determining unknown distances and positions. Since triangulation depends on knowing one side (baseline) and the angles from each end of that side to a distant point, the correct process and instruments must be used to achieve precise results. The angles measured are horizontal angles between two visible points.

Instruments used:

Theodolite – most commonly used for accurate angle measurement.
Total Station – a modern version of the theodolite with digital angle reading and distance measurement.
Telescope with graduated circle – used in older or simpler methods.

Step-by-step procedure to measure angles:

Select and mark the stations
Choose clear and stable ground for the triangle corners. Install ranging rods or signals at all points to be observed. The station where the instrument will be placed must be stable and well-marked.
Set up the theodolite

Place the theodolite exactly over the station point using a plumb bob or optical plummet.
Level the instrument using foot screws and the spirit level to make sure it is perfectly horizontal.
Focus the telescope clearly on the target.

Sight the first point (backward station)

Rotate the telescope and set it precisely on the first known point.
Lock the horizontal circle to zero or read the initial angle.

Measure the angle to the second point (forward station)

Unlock the horizontal circle and rotate the telescope to sight the second known point.
Lock the position and read the angle displayed on the theodolite.

Repeat for accuracy

The process is repeated several times, often by changing the face of the instrument (face left and face right). This reduces instrument and observational errors.
Average of multiple readings is taken as the final angle.

Important points during measurement:

Always ensure the instrument is centered and leveled correctly.
Use fine focusing for clear sights.
Take multiple readings to minimize human and instrument error.
Avoid angle measurement when there is heavy wind or vibration.

Use of measured angles:

Once the angles are measured from both ends of a known baseline, they are used along with trigonometric rules (such as sine rule) to compute unknown side lengths and point positions. This is how large areas are surveyed accurately by just measuring one baseline and many angles.

Conclusion

Measuring angles in triangulation involves setting up instruments like a theodolite at each station and carefully observing the angles between known points. This method, when done properly, allows surveyors to calculate distances and positions without having to physically measure every line, making triangulation a powerful and efficient surveying technique