Appendix D: Trigonometry
A knowledge of elementary trigonometry–the branch of mathematics that deals with the relationships between the sides and angles of triangles–is essential to a complete understanding of mechanics.
Consider the right-angled triangle (one angle is 90E) shown below.
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We first make the following observations:
Sides A and B join to form the right angle.
Side A is opposite to angle 2
Side B is adjacent to angle 2.
Side R is opposite to the right angle. This side is called the hypotenuse, and it is longer than sides A or B.
In addition we have the following basic laws.
The sum of all three angles is 180E.
R2 = A2 + B2 (The Pythagorean Theorem)
Now consider what happens if we expand or shrink the triangle. The length of the sides will change. However, the angles will remain the same and the ratios of the sides remain the same. For a right triangle the ratio of the sides are related to the angles by the trigonometric functions. We define the trigonometric functions as follows:
The values of these trigonometric functions are tabulated in Appendix E. Consider the following examples.
1. Determine the lengths of sides A and B in the triangle below.
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In
this example we know two angles and the length of the hypotenuse. 
2. Determine the angle 2 in the triangle below.
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In this example we know two sides and one angle of the right-angled triangle. We know
If we examine the table in Appendix E, we find that the angle 37E gives a value of tangent that is very close to 0.75. Therefore
