What is the purpose of trigonometry in the fields of surveying navigations engineering and other branches of physical sciences?

Answer 1

Trigonometry helps surveyors determine sides of a triangle which are either inaccessible or difficult to access. Knowing the length of a single base line enables the surveyor to define the other elements of the triangle by measuring the angle to the inaccessible points from accessible points.

Consequently the heights of trees and tall buildings can be determined by knowing the distance to the base of the tree or building. Similarly locations separated by, for example, rivers or busy roads can be determined by angular measurement from positions of known distance apart on the other side of the obstruction.

Survey control marks used for the mapping of countries were in the past established by triangulation from a known base line.

These days much of the survey control is undertaken using GPS equipment which uses satellite signals to determine positions on earth. However the theory behind the location of these positions also uses trigonometry and spherical trigonometry.