CK12 - Geometry

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Acuteand ObtuseTriangles

LearningObjectives

• Identifyand use the Law of Sines.


• Identifyand use the Law of Cosines.

Introduction

Trigonometryis mostcommonlylearnedon right triangles,but the ratioscan haveusesfor othertypesof
triangles,too. This lessonfocuseson how you can applysine and cosineratiosto anglesin acuteor obtuse

triangles.Rememberthat in an acutetriangle,all anglesmeasureless than. In an obtusetriangle,

therewill be one anglethat has a measurethat is greaterthan.

The Law of Sines

TheLaw of Sinesstatesthat in any triangle,the ratio of the lengthof a side to the sine of the angleopposite
it will be constant.That is, the ratio is the samefor all threeanglesand their oppositesides.Thus,if you
find the ratio,you can use it to find missinganglemeasureand side lengths.

Notethe conventionthat denotes and is the lengthof the side opposite.

Example 1