CK12 - Geometry

Sineand CosineRatios

LearningObjectives

• Reviewthe differentpartsof right triangles.


• Identifyand use the sine ratio in a right triangle.


• Identifyand use the cosineratio in a right triangle.


• Understandsine and cosineratiosin specialright triangles.

Introduction

Now that you havesomeexperiencewith tangentratiosin right triangles,thereare two otherbasictypesof
trigonometricratiosto explore.Thesineandcosineratiosrelateoppositeand adjacentsidesof a triangle
to the hypotenuse.Usingthesethreeratiosand a calculatoror a tableof trigonometricratiosyou can solve
a wide varietyof problems!

Review:Partsof a Triangle

The sine and cosineratiosrelateoppositeand adjacentsidesto the hypotenuse.You alreadylearnedthese
termsin the previouslesson,but they are importantto reviewand committo memory. The hypotenuseof
a triangleis alwaysoppositethe right angle,but the termsadjacentand oppositedependon whichangle
you are referencing.A side adjacentto an angleis the leg of the trianglethat helpsform the angle.A side
oppositeto an angleis the leg of the trianglethat doesnot help form the angle.

Example 1

Examinethe trianglein the diagrambelow.

Identifywhichleg is adjacentto angle ,whichleg is oppositeto angle ,and whichsegmentis the
hypotenuse.

The first part of the questionasks you to identifythe leg adjacentto. Sincean adjacentleg is the one

that helpsto form the angleand is not the hypotenuse,it mustbe. The next part of the questionasks

you to identifythe leg opposite. Sincean oppositeleg is the leg that doesnot help to form the angle,

it mustbe. The hypotenuseis alwaysoppositethe right angle,so in this triangleit is segment.

The SineRatio

Anotherimportanttrigonometricratio issine. A sine ratio mustalwaysreferto a particularanglein a right
triangle.The sine of an angleis the ratio of the lengthof the leg oppositethe angleto the lengthof the hy-
potenuse.Rememberthat in a ratio,you list the first item on top of the fractionand the seconditem on the
bottom.