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SOME COMMON SENSE FORMULAS
IF YOU KNOW TWO SIDES And you want to know an angle. * 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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