Dr. Math Does Trigonometry

Introduction to TrigonometryPart 1If you know 2 sides of a right triangleYou can find the third side.A + B = CB = C - AA = C - BACBabIf you know 2 angles You can find the missing angle.ma = 180 - (90 + mb)mb = 180 - (90 + ma)

ACBabWhat if you know one side & one angle and you want to find the missing sides?Now you need to use trigonometry!First we have to learn some vocabulary.Some vocabulary:The hypotenuse (hyp) is the longest side of the triangle it is always across from the right angleThe opposite (opp) is the side directly across from the reference angle The adjacent (adj) is the side next to the reference angleA picture always helpsLet b be your reference angleACBbadjhypoppbC is always the hypotenuseA is the adjacent side (next to the angle)B is the opposite side (across from the angle)LongestNextAcrossBut if we switch anglesNow let a be your reference angleACBaopphypadjaC is always the hypotenuseA is the opposite (across from the angle)B is the adjacent (next to the angle)LongestAcrossNextLets practice label each side relative to the reference angle.

Trigonometry uses ratios of the sidesThere are three sets of ratios for any trianglesinshort for sinecosshort for cosinetanshort for tangent

So what are the formulas?

SOH

CAHTOASin is Opposite over HypotenuseCos is Adjacent over HypotenuseTan is Opposite over AdjacentIf you need more help in memorizingSoh-Cah-ToaSome old horse Caught another horse Taking oats away.Some old horse Caught another horse Trotting on asphalt.

Calculating a side if you know the angleyou know a side (adj) and an angle (25)we want to know the opposite side

A CB = 625b

And one sin examplefind the length of side AWe have the angle and the hyp, and we need the opp

C = 2025bBA

What are the steps for doing one of these questions?Label the sidesChoose SOH, CAH, or TOASolve the equation for the unknown valueDoes the answer make sense?