Setup Control Points (Survey Radial) using Sierrasoft Topko

A surveyor wants to measure a property that is roughly in the shape of a polygon, finding its perimeter and area.

A widely used method is to make a radial survey. The surveyor picks a point inside the polygonal area and measures the distance from that point to each of the vertices of the polygon

The lengths of the radial lines are then measured precisely, and the angles between them as well - either measuring directly, or by finding the true bearings of each radial line and finding differences. With this information the lengths of the boundary segments can be calculated using the cosine rule. The area of each triangle formed by two radial lines and a boundary segment can then be calculated using the sine area formula. The surveyor is then able to report the total length of the boundary and also the area enclosed

The cosine rule

If the three side lengths in a triangle are $$a, $$b and $$c, with an angle $$C opposite the side with length $$c, then

c^2=a^2+b^2-2ab\cos C

The sine rule

If a triangle has two side lengths $$a and $$b, and $$C is the known angle between them, then

Area = 1/2ab sin C

Now we use software Topko as below Picture as below

New Points points = 10x Measurement

Old Points = 5x Measurements

Step by Step Calculation Survey Radial as below