Previous Section | Table of Contents | Next Section
11.0.0 APPENDIX C: USING TRIGONOMETRIC LAWS AND FUNCTIONS TO SOLVE SURVEYING PROBLEMS
11.1.0 The Law of Cosines
11.2.0 The Law of Sines
11.3.0 Trigonometric functions for right triangles
11.1.0 THE LAW OF COSINES
Trigonometric functions and laws are frequently used in surveying, and are especially useful in determining distances between points which cannot be measured directly. With the aid of a pocket calculator with trigonometric functions, the Law of Cosines can be used to solve a triangle of which one angle and two sides are known. In any triangle ABC:
11.1.1 In triangle ABC (Figure 11.1), three points must be located relative to each other. With the transit located at C, the distances AC and BC can be measured, as well as the angle between them. The distance between A and B cannot be hand measured. Side a = 110', b = 150', and LC = 75°. Find AB:
Figure 11.1: Using the Law of Cosines to find side c of triangle ABC.
11.2.0 THE LAW OF SINES
This law can be used to compute unknown sides of a triangle if two angles have been determined with a transit, and the length of one side is known:
11.2.1 In triangle DEF (Figure 11.2), angle D = 35°, angle E = 65°, and side f = 160 feet; find sides d and e. First find angle F = 180° - (35° + 65°) = 80°. Side e can now be calculated:
Figure 11.2: Using the Law of Sines twice to
determine the unknown sides of a triangle,
if two angles and the side between them are known. |
Use original measurements
to find side d:
|
11.3.0 TRIGONOMETRIC FUNCTIONS FOR RIGHT TRIANGLES
Figure 11.3: A right triangle in which r is the hypotenuse, y is the
side opposite sine, and x is the side adjacent to sine.
Previous Section | Table of Contents | Next Section
|
