IF YOU KNOW TWO SIDES
And you want to know an angle.
Use Sketch Below(from page 8)

* If you know the legs only use the inverse tangent.
                   Examples:

                   tan-1(Lleg ÷ Sleg) = Langle
                   tan‑1(Sleg ÷ Lleg) = Sangle

* If you know a leg and the hypotenuse use either inverse sine (sin‑1) or inverse cosine (cos‑1) depending on what angle you want.
                   Examples:

                   sin‑1(Sleg ÷ Hyp) = Sangle
                   sin‑1(Lleg ÷ Hyp) = Langle
                   cos‑1(Sleg ÷ Hyp) = Langle
                   cos‑1(Lleg ÷ Hyp) = Sangle
Never divide the Hypotenuse by a leg. (Hyp ÷ leg)! It gives a wrong ratio for our use.

IF YOU KNOW AN ANGLE AND A SIDE
And you want to know another side.

* If you know a leg and an angle and want to know the other leg always use tangent.
                   Examples:

                   tan(Sangle) x Lleg = Sleg
                   tan(Langle) x Sleg = Lleg
Note the ratios: tan(Sangle) is always less than one, So when you multiply it times the larger leg it will give you something shorter. tan(Langle) is always greater than one. When you multiply it times the smaller leg you will get something longer.

* If you know a leg and an angle and want to know the hypotenuse divide the legs by sine or cosine of an angle.
                   Examples:

                   Sleg ÷ sin(Sangle) = Hyp
                   Sleg ÷ cos(Langle) = Hyp
                   Lleg ÷ sin(Langle) = Hyp
                   Lleg ÷ cos(Sangle) = Hyp

                  
* If you know the hypotenuse and an angle use either Sine or Cosine.
                   Examples:

                   sin(Sangle) x Hyp = Sleg
                   sin(Langle) x Hyp = Lleg
                   cos(Sangle) x Hyp = Lleg
                   cos(Langle) x Hyp = Sleg
Notice how the sine or cosine of an angle is always less than one. Remember ratio. The legs are always smaller than the hypotenuse. This number must be less than one so that when you multiply it times the hypotenuse you will always get something shorter than the hypotenuse.

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