CK12 - Geometry

• Understandtangentratiosin specialright triangles.

Introduction

Now that you are familiarwith right triangles,the ratiosthat relatethe sides,as well as otherimportantap-
plications,it is time to learnabouttrigonometricratios.Trigonometricratiosshowthe relationshipbetween
the sidesof a triangleand the anglesinsideof it. This lessonfocuseson the tangentratio.

Partsof a Triangle

In trigonometry, thereare a numberof differentlabelsattributedto differentsidesof a right triangle.They
are usuallyin referenceto a specificangle.The hypotenuseof a triangleis alwaysthe same,but the terms
adjacentandoppositedependon whichangleyou 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.

In the triangleshownabove,segment is adjacentto , and segment is oppositeto.

Similarly, is adjacentto , and is opposite. The hypotenuseis always.

Example 1

Examinethe trianglein the diagrambelow.

Identifywhichleg is adjacentto ,oppositeto ,and 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 trianglethe hypotenuseis