Right Triangle Application Problems Solved

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1/7/2016 RightTriangleApplicationProblemsSolvedhttp://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 1/3RightTriangleApplicationsProblemsSolved1.A16footladderisleaningagainstahouse.Ittouchesthebottomofawindowthatis12feet6inchesabovetheground.Whatisthemeasureoftheanglethattheladderformswiththeground?Letxequalthemeasureoftheangletheladderformswiththeground.Apictureoftheproblemisdrawntotheright.Wehavethesideoppositetotheangleinquestionaswellasthehypotenuse.Icanwritetheunknownintermsoftheknownusingthedefinitionofsine:.FirstIneedtogeteverythingintermsofinches:12ft=144in.,so12ft6in=150in.and =192inso .Noticetheunitscancelout.Youshouldalwaysgetaunitlessnumberwhenyouhaveatrigonometricratio.UsingtheinversesinonacalculatorIgetthemeasureoftheangleisequalto .2.a.IwouldusetheconverseofthePythagoreanTheoremtosolvethisproblem.b.TheconverseofthePythagoreanTheoremtellsmethatifthenthepolewouldbeatarightanglewiththegroundwhenthestringwas17ft.Socomputeand since thepolewouldbeatarightanglewiththegroundwhenthestringis17ft.3.Kailaisflyingakitewhosestringismakinga anglewiththeground.Thekitestringis65meters1/7/2016 RightTriangleApplicationProblemsSolvedhttp://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 2/3long.Howfaristhekiteabovetheground?AfterreadingtheproblemIwoulddrawthefollowingpicture:wherehistheheight,whatIwanttofind.Iknowanangle,soIknowIneedtouseatrigonometricratiotosolvethisproblem.IamlookingforthesideoppositethegivenangleandIknowthehypotenuse.LookingatmydefinitionsIseeIshouldusethesineratiotowritetheunknownintermsofknowns.SoIhaveor .Sousingmycalculatortocomputesin Ifindthekiteisapproximately61metersabovetheground.4.TheBrook'sareinstallingawidescreentelevisionwitha60inchdiagonal.Theirentertainmentcenteris48incheswideby36incheshigh,willthetelevisionfitintheircurrententertainmentcenter?AfterreadingtheproblemIdrawthefollowing:Iwanttofinddtoseeifthetelevisionwitha60inchdiagonalwillfitintoarectanglethatis48inchesby36inches.IcanusethePythagoreanTheoremtoputmyknownsintermsofmyunknown:orsothetelevisionwillfitexactly.5.Asurveyoris100metersfromthebaseofadam.Theangleofelevationtothetopofthedammeasures .Thesurveyor'seyelevelis1.73metersabovetheground.Findtheheightofthedamtothenearesthundredthofameter.1/7/2016 RightTriangleApplicationProblemsSolvedhttp://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 3/3AfterreadingtheproblemIdraw:Sothetopofthedamwillbedistanced+1.73m.Ihaveandangle,andthesideadjacenttotheangleandIamlookingforthesideoppositetheangle.SinceIwillusethistrigonometricratiotosolveford.Iget:Iamnotquitedone,ImustaddthedistancethetriangleisabovethegroundtogettheheightIamlookingfor.Theheightofthedamis48.77m+1.73m=50.50m.Return