In this lesson, you will learn how to use trigonometry.
TERMINAL LEARNING OBJECTIVE:
You will be taught how to use trigonometry in surveying operations.
You will be given the material contained in this lesson.
You will correctly answer the practice exercise questions at the end of this lesson.
REFERENCES: The material contained in this lesson was derived from TM 5-232, FM 5-233,
NAVEDTRA 10696, CDC 3E551A, and Appendix C of this ACCP.
Surveyors work almost daily with the triangle in surveying vast expanses of land. In doing so, they use
a network of triangles, which is known as triangulation. The sides and angles of a plane triangle are so
related that given any three parts, provided at least one of them is a side, the shape and size of a triangle
can be determined. This science, which is called trigonometry, is both geometric and algebraic in
nature. This branch of mathematics deals with computing unknown parts. It begins by showing the
mutual dependence of the sides and angles in a triangle and, for that purpose, employs the ratio of the
sides in a right triangle. It is based on the properties of similar triangles and is applied whenever angles
enter into the solution of the problem. Because trigonometry deals primarily with angles, it is necessary
for the surveyor to have a clear conception of the meaning and the measurement of angles.
PART A - ANGLES
4-1. Defining Angles. An angle is defined as the figure formed by the intersection of two lines at one
point. The point is called the vertex of the angle. The two lines forming the angle are called the sides or
legs of the angle. The angle, as it applies to trigonometry, is read by designating the capital letter placed
at the vertex. The mathematical symbol for the word angle is simply a small . The size of magnitude
of an angle is determined by