Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 17: Geometry at Work 241

The ratio of the side opposite the 25r angle to the hypotenuse is the same in every right triangle
in the 25r family. The ratios of other pairs of sides will remain constant throughout the 25r
family, and it’s not limited to just the 25r family. The ratios of pairs of sides are the same for all
the right triangles in any family. Trigonometry takes advantage of that fact and gives a name to
each of the possible ratios.

If the three sides of the right angle are labeled as the hypotenuse, the side opposite a particular
acute angle, A, and the side adjacent to the acute angle A, six different ratios are possible. Three
are commonly used. The other three are the reciprocals of the first three, and while it’s nice to
know they exist in case you ever need them, you can just deal with the three basic ratios called
the sine, cosine, and tangent.

1

     

opposite1

opposite1 - hypotenuse2 opposite2 - hypotenuse1

opposite1 - hypotenuse2 opposite2 - hypotenuse1

opposite1 - hypotenuse2

opposite1 - hypotenuse2

hypotenuse1

hypotenuse1

1 hypotenuse2

hypotenuse1 hypotenuse2

hypotenuse1

hypotenuse1

hypotenuse1 - hypotenuse2

opposite2 hypotenuse2

opposite2

opposite1

opposite2

opposite2

Opposite A Hypotenuse
Adjacent to B

Adjacent to B

Opposite A

B

CA

sin(A)

opposite

hypotenuse

cos(A)

adjacent

hypotenuse

tan(A)

opposite

(^5) adjacent
Getting the definitions of the three principal trig ratios right is critical for your problem solving,
so it helps to have a memory device, or mnemonic, to help you remember them. Many people like
the word SOHCAHTOA to remember the trig ratios. It stands for Sine = Opposite/Hypotenuse;
Cosine = Adjacent/Hypotenuse; Tangent = Opposite/Adjacent.