What Is Trigonometric Surveying?

What Is Trigonometric Surveying?

Trigonometric surveying uses trigonometric functions to determine distances and angles on any plane. It can be used to measure horizontal and vertical angles, side lengths, triangle circumferences and line distances.

Trigonometric surveying is a survey of an area of land conducted by measuring a single base and connecting it to other points in the tract studied by a series of triangles, the angles of which are precisely recorded, and the relative positions and distances of all components estimated from these data.

How To Conduct A Trigonometric Survey

Geodetic or trigonometric surveying takes into consideration the curvature of the earth because big areas and long distances are involved.

Geodetic surveying employs highly sophisticated tools and processes. Geodetic work is carried out by the state agency.

The goal of geodetic surveying is to precisely estimate the relative location of a system of widely spaced points (stations) on the earth’s surface and their absolute positions.

The relative positions are determined by the azimuths and lengths of the f lines that connect them. Absolute positions are established by latitude and longitude, as well as elevation above mean sea level.

Geodetic surveying employs the following methods:

  • Triangulation (most accurate but expensive)
  • Precise traverse (inferior and utilized when triangulation is physically impossible or prohibitively expensive), for example, in densely forested region.


Triangulation is based on the trigonometry assumption that one side and three angles can be determined using the since rule.

This method selects and establishes suitable sites known as triangulation stations throughout the area to be surveyed. A series of triangles or a chain of quadrilaterals can connect the stations.

Baseline: Whose length is measured? These stations serve as the vertices of a sequence of mutually connected triangles, the entire figure being referred to as the ‘Triangulation system.’

In this triangle system, one line, say ‘AB,’ and all the angles are carefully measured, and the lengths of all the remaining lines in the system are determined. Another line, say GH, is very properly measured at the conclusion of the system to check both the fieldwork and the computation.

The line whose length is really measured is referred to as the baseline or base, and the line whose length is measured for checking purposes is referred to as the check base.

Figures for Triangulation: The geometric figures utilized in the triangulation scheme are as follows:

  • Triangular shapes
  • Quadrilaterals
  • Quadrilaterals, Pentagons, and hexagons having a central axis.

This design, while simple and affordable, is less accurate due to the small number of circumstances involved in its adjustment.

  1. Station adjustment ==> sum of angles is 180
  2. Figure adjustment ==> sum of angles is 400 grad or 360
  3. Quadrilateral adjustment ==> sum of angles is 400 grad or 360 (all the angles are horizontal)

With central stations, quadrilaterals, pentagons, or hexagons are used. A chain of quadrilaterals can be utilized for extremely exact work.

There is no station at the diagonal intersection. This approach is the most accurate since it adjusts for a bigger number of conditions.

Triangles should be well-shaped or well-proportioned to reduce the influence of slight errors in angle measurement, i.e., they should not have angles less than 30 or larger than 120. The best triangle shape is an equilateral triangle, and the best quadrilateral shape is a square.

Trigonometric Leveling

Trigonometric leveling is a kind of surveying in which we determine the vertical distance between two places using measurements of vertical angles and known distances.

The known distances are considered to be horizontal or geodetic lengths at mean sea level (MSL). Distances are measured directly (as in plane surveying) or computed (as in geodetic surveying).

Trigonometric leveling can be accomplished in two ways.

  1. Height and distance measurements were taken.

If possible, we can estimate the horizontal distance between the specified sites here.

We observe the vertical angles and then use them to calculate distances. If the distances are great enough, we must supply the correction for curvature and refraction, which we do linearly to the calculated distances.

  • Observations on the Geodetic.

The distances between the two points i.e., geodetic observations, are geodetic distances, and the concepts of plane surveying do not apply here. Curvature and refraction adjustments are applied directly to the angles.

The methods of observation in Trigonometric levelling are:

  • Direct Method- This method is beneficial when it is not possible to position the instrument over the station whose elevation is to be calculated.

For example, to determine the tower’s height. The device is placed on the ground at a known elevation station in this manner.

  • Reciprocal Method- In this procedure, the instrument is alternately placed on each of the two stations, and observations are made.

The elevation difference between two stations A and B must be established.

Great Trigonometrical Survey

The Great Trigonometrical Survey was a scientifically precise survey of the whole Indian subcontinent. It was founded in 1802 under the patronage of the East India Company by British military officer William Lambton.

The project was given to the Survey of India under the direction of his successor, George Everest. Andrew Scott Waugh succeeded Everest, and after 1861, the project was supervised by James Walker, who oversaw its completion in 1871.

Among the Survey’s many achievements were the division of British holdings in India and the measuring of the heights of the Himalayan giants: Everest, K2, and Kanchenjunga.

The Survey also had a huge scientific impact, as it was responsible for one of the first exact measurements of a segment of an arc of longitude, as well as observations of the geodesic anomaly, which contributed to the creation of isostasy theories.

The native surveyors used in the Himalayas, particularly in Tibet (where Europeans were not permitted), were known as pandits, and among them were the cousins Nain Singh Rawat and Krishna Singh Rawat.

Instruments and methods used

A few properly measured baselines and a sequence of angles were used in triangulation surveys. The original baseline was carefully measured because the accuracy of the future survey was crucial.

Several modifications were made, the most important of which was the temperature. A particularly precise folding chain was used, which was put on horizontal tables, all protected from the sun and under constant tension.

The early surveys used the theodolites produced by William Carey, a Zenith sector made by Jesse Ramsden, and 100-foot (30 m) chains. Later surveys made use of theodolites that were more compact.

Accurate instruments could not always be bought through the regular government contracting system, and Everest personally oversaw instrument construction.

In Calcutta, he had a craftsman, Henry Barrow, set up an instrument company. Barrow was succeeded by Syed Mohsin of Arcot, and following his death, Cooke of York supplied the instruments.

Correcting Mistakes

A number of corrections were applied to all distances calculated using simple trigonometry in order to attain the highest accuracy:

  • The earth’s curvature
  • The curvature of the earth’s surface is not spherical.
  • Mountains’ gravitational pull-on pendulums and plumb lines.
  • Refraction.
  • Elevation above sea level

Trigonometric Surveying Applications

The main applications of Trigonometric Surveying are

a. Laying out roads, railroads and other physical structures

b. Mapping the terrain

c. Planning urban areas

d. Estimating the height of land (used in flood mapping as well)

e. Estimating the locations of ore bodies, oil and natural gas deposits etc. to help in their exploitation.

Trigonometric Surveying Instruments

Instruments used are but not limited to:

a. The Theodolite- This instrument is usually a telescope for measuring horizontal angles.

b. The sextant- This is a small parabolic mirror mounted on four arms with setting circles, used for measuring the altitude of the sun, Polaris or stars.

c. The Horizontal Transit- This instrument is used to measure the altitude difference between two points in reference to an eyelet and by comparing it with a scale on the transit attached to the vertical staff and moving over it while observing the two pointers in an eyepiece of a theodolite.

d. The Prismatic Compass- This is a surveying instrument with a compass, usually mounted on a telescope, used to measure the angle between two points.

e. The Compass- This is an instrument for making the angles of elevation and azimuth on extension lines with a sinusoidal compensating screw.

f. The Geodetic Surveyor’s transit- This is an instrument for measuring the angle between two points of reference in reference to an eyelet, using a probe and compensating screw.

g. The level- This is an instrument used to measure the earth’s vertical angle.

h. The electronic distance meter is a surveying instrument for measuring distances, usually with a precision of 6 inches (150 millimeters) or 1 millimeter.

i. Magnetic compass- This is a compass used in survey work. It is adjusted to the magnetic meridians of the earth and the barometric altitudes of mean sea level.

j. Ocular micrometer- This is an instrument for measuring the angle between two points in reference to an eyelet, using a probe with a micrometer screw.

Trigonometric Surveying Benefits

The benefits of trigonometric surveying are immense, from land mapping and charting, to locating mineral deposits.

The main benefits are:

a. More Accurate Maps- Trigonometric Surveying allows you to get extremely accurate maps, where even the smaller details are accounted for. This leads to understanding our environment better and increased safety.

b. Faster Survey Times- Since trigonometric surveying (usually) involves fewer people and is made easier by advanced technology, the whole process is significantly faster.

c. More efficient- Trigonometric surveying is an extremely efficient technology, which means fewer mistakes and as a result, better quality work.

Trigonometric Surveying Con’s

Of course, no one can deny that trigonometric surveying has its cons and pros.

Some of the cons are:

a. More expensive- The main con to Trigonometric Surveying is that it’s more expensive than other Surveying techniques. It requires more purchases of instruments, and thus more money.

b. The tools are delicate- The instruments are very delicate and breakable. Since these tools must be carried by several people, they tend to end up breaking much more often than they do in traditional Surveying techniques.

c. The tools are heavy- It is much more difficult to carry a lot of instruments and equipment in the mountains, since there are more places where they can be broken.

d. Harder to get people- Since Trigonometry Surveying is more advanced than traditional Surveying techniques, it’s harder to get people in general.

e. Harder to complete the survey- Since Trigonometry Surveying is generally more advanced, it requires considerably more time to complete the survey.


What do you mean by trigonometric surveying?

This is a survey of an area of land conducted by measuring a single base and connecting it to other points in the tract studied by a series of triangles, the angles of which are precisely recorded, and the relative positions and distances of all components estimated from these data

How is trigonometry used in surveying?

When measuring the height and angles of land, trigonometry is applied. It can be used to calculate the height from a given position to a mountain, the distance between two trees, and the distance between lakes.

What is trigonometric levelling?

It is an indirect method of leveling in which the difference in elevation between the sites is calculated using the observed vertical angles and measured distances.

It is often used in topographical work to determine the heights of the tops of structures, chimneys, and churches, among other things.

Which instrument is used in trigonometric survey?

A theodolite, which is an equipment having a telescope attached to two rotating circles (one horizontal and one vertical) to measure the horizontal and vertical angles, is used to measure the angles in the triangles.

What are the advantages of trigonometric levelling?

When exact elevations are unavailable or the elevations of inaccessible sites must be established, trigonometric leveling is frequently required.

Triangulation is used to determine the horizontal location of an unknown point based on two known points of position and elevation.

Who started great trigonometric survey?

On 10 April 1802, the Great Trigonometrical Survey of India began with the measuring of a baseline near Madras. Major Lambton chose the low plains, which include St. Thomas Mount to the north and Perumbauk Hill to the south.

The baseline measured 7.5 miles (12.1 kilometers).

What math do building surveyors use?

Trigonometry which is a branch of mathematics that helps us find angles and distances. It is widely utilized in science, engineering, video games, and other fields.

Sine, Cosine, and Tangent are the three main functions in trigonometry. They are nothing more than one side of a right-angled triangle divided by another.

Do you need to be good at math to be a surveyor?

Although measuring quantities is an important aspect of quantity surveying, the mathematical requirements are quite simple. When giving numbers and cost estimates, the surveyor will also apply some math.

But, once again, while they must be numerate, the mathematics is not particularly difficult.

Who started survey from Chennai to Himalayas?

The Great Trigonometrical Survey (1802–1852) was launched on 10 April 1802 by British surveyor Col. William Lambton from St. Thomas Mount in Chennai to the Himalayan foothills.

How is trigonometry used in construction?

Trigonometry allows architects to calculate roof slopes, ground surfaces, light angles, structural loads, and the height and width of structures to create a mathematical draft that a builder may use.

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