Right Triangle Application Problems Solved

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<ul><li><p>1/7/2016 RightTriangleApplicationProblemsSolved</p><p>http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 1/3</p><p>RightTriangle</p><p>Applications</p><p>ProblemsSolved</p><p>1.A16footladderisleaningagainstahouse.Ittouchesthebottomofawindowthatis12feet6inchesabovetheground.Whatisthemeasureoftheanglethattheladderformswiththeground?</p><p>Letxequalthemeasureoftheangletheladderformswiththeground.Apictureoftheproblemisdrawntotheright.</p><p>Wehavethesideoppositetotheangleinquestionaswellasthehypotenuse.Icanwritetheunknownintermsoftheknownusingthedefinitionofsine:</p><p>.FirstIneedtogeteverythingintermsofinches:12ft=144in.,so12ft6in=150in.and =192inso .Noticetheunitscancelout.Youshouldalwaysgeta</p><p>unitlessnumberwhenyouhaveatrigonometricratio.UsingtheinversesinonacalculatorIgetthemeasureoftheangleisequalto .</p><p>2.</p><p>a.IwouldusetheconverseofthePythagoreanTheoremtosolvethisproblem.</p><p>b.TheconverseofthePythagoreanTheoremtellsmethatifthenthepolewouldbeatarightanglewith</p><p>thegroundwhenthestringwas17ft.</p><p>Socompute</p><p>and since thepolewouldbeatarightanglewiththegroundwhenthestringis17ft.</p><p>3.Kailaisflyingakitewhosestringismakinga anglewiththeground.Thekitestringis65meters</p></li><li><p>1/7/2016 RightTriangleApplicationProblemsSolved</p><p>http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 2/3</p><p>long.Howfaristhekiteabovetheground?</p><p>AfterreadingtheproblemIwoulddrawthefollowingpicture:</p><p>wherehistheheight,whatIwanttofind.Iknowanangle,soIknowIneedtouseatrigonometricratiotosolvethisproblem.IamlookingforthesideoppositethegivenangleandIknowthehypotenuse.LookingatmydefinitionsIseeIshouldusethesineratiotowritetheunknownintermsofknowns.</p><p>SoIhave</p><p>or .</p><p>Sousingmycalculatortocomputesin Ifindthekiteisapproximately61metersabovetheground.</p><p>4.TheBrook'sareinstallingawidescreentelevisionwitha60inchdiagonal.Theirentertainmentcenteris48incheswideby36incheshigh,willthetelevisionfitintheircurrententertainmentcenter?</p><p>AfterreadingtheproblemIdrawthefollowing:</p><p>Iwanttofinddtoseeifthetelevisionwitha60inchdiagonalwillfitintoarectanglethatis48inchesby36inches.IcanusethePythagoreanTheoremtoputmyknownsintermsofmyunknown:</p><p>or</p><p>sothetelevisionwillfitexactly.</p><p>5.Asurveyoris100metersfromthebaseofadam.Theangleofelevationtothetopofthedammeasures .Thesurveyor'seyelevelis1.73metersabovetheground.Findtheheightofthedamtothenearesthundredthofameter.</p></li><li><p>1/7/2016 RightTriangleApplicationProblemsSolved</p><p>http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 3/3</p><p>AfterreadingtheproblemIdraw:</p><p>Sothetopofthedamwillbedistanced+1.73m.Ihaveandangle,andthesideadjacenttotheangleandIamlookingforthesideoppositetheangle.Since</p><p>Iwillusethistrigonometric</p><p>ratiotosolveford.</p><p>Iget:</p><p>Iamnotquitedone,ImustaddthedistancethetriangleisabovethegroundtogettheheightIamlookingfor.Theheightofthedamis48.77m+1.73m=50.50m.</p><p>Return</p></li></ul>