# Trigonometry Trigonometry Ratios for Right Angle Triangles The Ratios SOH CAH TOA Sine = opposite hypotenuse Cosine = opposite hypotenuse Tangent = opposite adjacent Sin = O

H Cos = A H Tan = O A Steps to Solve Right Triangles Trig Formulas: SOH CAH TOA

Step 1: Labelling Sides Step 2: Setting up the Formula Step 3: Solving the Formula Which Ratio to use? 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 Step 1: Label the sides 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 Opposite Adjacent Step 2: Set up the Formula Decide what formula to use once your sides have been labeled. Step 3: Solve the Formula

Use the formula that has opposite and hypotenuse SOH Sin = O Sin 35 = opp H 9 9(Sin 35) = opp 5.2 = opp

Solve for x Step 1: Labelling Sides Step 2: Setting up the Formula We know Opp and Hyp SOH Step 3: Solving the Formula

Sin = O H Sin70 = 6 x=6 x Sin70 x = 6.4 Solve for x Step 1: Labelling Sides Step 2: Setting up the Formula

We know Opp and Adj TOA Step 3: Solving the Formula Tan = O A

Tan x = 5 Tan x = 0.4167 12 Tan-1(0.4167)=x x = 22.6