Soh Cah Toa

Many people learn the rules for right-triangle trigonometry in high school. When I learned the definitions of sine, cosine and tangent, my teacher taught me to remember them like this: suppose you kick your desk in frustration over your math homework, and hurt your foot in the process -- you should go Soak A Toe (Ahhh!)

If you know the value of one of the two non-right angles in a right triangle, and the length of one of the sides, you can determine the lengths of the other two sides using sinq = o/h cosq = a/h tanq = o/a where "o" stands for the side of the triangle opposite to the known angle, "a" stands for the side of the triangle adjacent to the known angle, and "h" stands for the hypotenuse of the triangle.

There are some important rules that will help you to spot or avoid mistakes in calculations with these definitions:

• the adjacent and opposite sides are always shorter in length than the hypotenuse.
• the sine and cosine functions vary in value between zero and one (they are never larger, and come out positive if the angle is considered positive).
• the sine of zero degrees is zero; the sine of ninety degrees is one.
• the cosine of zero degrees is one; the cosine of ninety degrees is zero.

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