CK12 - Trigonometry

We can use this resultto determinethe measureof the anglesof a triangle.In particular, if we knowthe
measuresof two angles,we can alwaysfind the third.

Example3:Find the measuresof the missingangles.

a. A trianglehas two anglesthat measures 30
o
and 50
o
.

b. A right trianglehas an anglethat measures 30 o.

c. An isoscelestrianglehas an anglethat measures 50 o.

Solution:

a. 100o

180 - 30 - 50 = 100.

b. 60o

The triangleis a right triangle,whichmeansthat one anglemeasures 90 o.

So we have:180 - 90 - 30 = 60.

c. 50oand 80o, or 65oand 65o

Thereare two possibilities.First,if a secondanglemeasures 50

o

, then the third anglemeasures 80

o

as 180

• 50 - 50 = 80.

In the secondcase,the 50oangleisnotone of the congruentangles.In this case,the sum of the othertwo

anglesis 180 - 50 = 130. Thereforethe two angleseachmeasure 65 o.

Noticethat informationaboutthe anglesof a triangledoesnot tell us the lengthsof the sides.For example,
two trianglescouldhavethe samethreeangles,but the trianglesare notcongruent.That is, the correspond-
ing sidesand the correspondinganglesdo not havethe samemeasures.However, thesetwo triangleswill
besimilar.Next we definesimilarityand discussthe criteriafor trianglesto be similar.

Similartriangles

Considerthe situationin whichtwo triangleshavethreepair of congruentangles.