Ratios for Right Angle Triangles

 Sine = opposite hypotenuse  Cosine = opposite hypotenuse  Tangent = opposite adjacent Sin = OCos = ATan = O H H A

 Trig Formulas: SOH CAH TOA  Step 1: Labelling Sides  Step 2: Setting up the Formula  Step 3: Solving the Formula

 To determine the ratio that you need to use, you must first label the triangle.  How you label the triangle will depend on the information you are given.  Remember: Ratios are SOH CAH TOA

The triangle will have the 90° angle and one other angle labelled. The hypotenuse is always the side opposite to the 90° angle. The opposite side will be the side opposite to the marked angle. The last side is the adjacent side. Hypotenuse Adjacent Opposite

 Decide what formula to use once your sides have been labeled.

 Use the formula that has opposite and hypotenuse  SOH  Sin = OSin 35° = opp H9 9(Sin 35°) = opp 5.2 = opp

 Step 1: Labelling Sides  Step 2: Setting up the Formula ◦ We know Opp and Hyp  SOH  Step 3: Solving the Formula  Sin = OSin70° = 6x = 6 H x Sin70° x = 6.4

 Step 1: Labelling Sides  Step 2: Setting up the Formula ◦ We know Opp and Adj  TOA  Step 3: Solving the Formula  Tan = OTan x = 5 Tan x = A 12 Tan -1 (0.4167)=x x = 22.6°