2 Parts of a Right Triangle The hypotenuse will always be the longest side, and opposite from the right angle.Imagine that you are at Angle A looking into the triangle.The opposite side is the side that is on the opposite side of the triangle from Angle A.The adjacent side is the side next to Angle A.
3 Parts of a Right Triangle Now imagine that you move from Angle A to Angle B.From Angle B the opposite side is the side that is on the opposite side of the triangle.From Angle B the adjacent side is the side next to Angle B.
4 Review B A B A For Angle A Hypotenuse This is the Opposite Side This is the Adjacent SideAAdjacent SideAdjacent SideBFor Angle BHypotenuseThis is the Opposite SideThis is the Adjacent SideA
5 Trig Ratios Use Angle B to name the sides Using Angle A to name the sidesWe can use the lengths of the sides of a right triangle to form ratios. There are 3 different ratios that we can make.The ratios are still the same as before!!
6 Trig Ratios Each of the 3 ratios has a name HypotenuseEach of the 3 ratios has a nameThe names also refer to an angleOppositeAAdjacent
7 Trig Ratios If the angle changes from A to B HypotenuseIf the angle changes from A to BOppositeAThe way the ratios are made is the sameAdjacent
8 SOHCAHTOA B Hypotenuse Here is a way to remember how to make the 3 basic Trig RatiosOppositeAAdjacent1) Identify the Opposite and Adjacent sides for the appropriate angleSOHCAHTOA is pronounced “Sew Caw Toe A” and it meansSin is Opposite over Hypotenuse, Cos is Adjacent over Hypotenuse, and Tan is Opposite over AdjacentPut the underlined letters to makeSOH-CAH-TOA
9 Examples of Trig Ratios First we will find the Sine, Cosine andTangent ratios for Angle P.2012AdjacentNext we will find the Sine, Cosine, andTangent ratios for Angle QQ16OppositeRemember SohCahToa
10 Similar Triangles and Trig Ratios PB201253AQC4R16They are similar triangles, since ratios of corresponding sides are the sameLet’s look at the 3 basic Trig ratios for these 2 trianglesNotice that these ratios are equivalent!!
11 Similar Triangles and Trig Ratios Triangles are similar if the ratios of the lengths of the corresponding side are the same.Triangles are similar if they have the same anglesAll similar triangles have the same trig ratios for corresponding angles