Trigonometry - Triangle Notations

Trigonometry, which literally means "triangle measurement," is one of the most feared subjects in math that students learn, but it is much easier than they often give it credit for. (For some interesting background history and applications of trigonometry, wikipedia has a good article.) Trigonometry deals with the relationships between the angles and sides of triangles, especially triangles with one 90 degree angle (right-angle triangles). The longest side, opposite to the right angle, is called the HYPOTENUSE.

The standard convention of naming triangles is to name them by the letters of their 3 corners. So in this example, this is triangle ABC. Similarly, the sides are named by the corners at either end of the side, so here we have sides AB, BC, and AC. The corners may be named with a single letter, or designated by 3 letters representing the points that make up the angle, in order, with the corner point in the middle (ie. angle B = angle ABC, angle A = angle CAB, angle C = angle ACB).

An alternate way to look at triangles is to name the ANGLES with capital letters. Then, the side that is directly opposite the angle is given the same letter, but in lower case. Therefore, from the above example, side AC = side b, AB = c, and BC = a. Somewhat confusing, but! not really... it makes sense. The keyword in this method of ! notation is OPPOSITE.

In working with triangle sides and angles, you will be dealing with their names, but also their RELATIVE names... meaning that for angle B, you may be interested in it's OPPOSITE side and ADJACENT side. The opposite side is easy to identify... it is the side that does not touch the corner you are looking at. The hypotenuse is also easy... it is opposite the 90 degree angle, and will always be the longest side. The adjacent side is obviously the side that's left! It touches the corner, but is not the hypotenuse.

A solid understanding of the naming of angles and sides (in particular, the relative naming designations) is important before you can move on to do calculations involving these measurements. These calculations in themselves, however, are very straightforward, and as will be explained in a separate post, may be figured out very easily by remembering just one word - SOHCAHTOA.

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