Right Triangle Application Problems Solved

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  • 1/7/2016 RightTriangleApplicationProblemsSolved

    http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 1/3

    RightTriangle

    Applications

    ProblemsSolved

    1.A16footladderisleaningagainstahouse.Ittouchesthebottomofawindowthatis12feet6inchesabovetheground.Whatisthemeasureoftheanglethattheladderformswiththeground?

    Letxequalthemeasureoftheangletheladderformswiththeground.Apictureoftheproblemisdrawntotheright.

    Wehavethesideoppositetotheangleinquestionaswellasthehypotenuse.Icanwritetheunknownintermsoftheknownusingthedefinitionofsine:

    .FirstIneedtogeteverythingintermsofinches:12ft=144in.,so12ft6in=150in.and =192inso .Noticetheunitscancelout.Youshouldalwaysgeta

    unitlessnumberwhenyouhaveatrigonometricratio.UsingtheinversesinonacalculatorIgetthemeasureoftheangleisequalto .

    2.

    a.IwouldusetheconverseofthePythagoreanTheoremtosolvethisproblem.

    b.TheconverseofthePythagoreanTheoremtellsmethatifthenthepolewouldbeatarightanglewith

    thegroundwhenthestringwas17ft.

    Socompute

    and since thepolewouldbeatarightanglewiththegroundwhenthestringis17ft.

    3.Kailaisflyingakitewhosestringismakinga anglewiththeground.Thekitestringis65meters

  • 1/7/2016 RightTriangleApplicationProblemsSolved

    http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 2/3

    long.Howfaristhekiteabovetheground?

    AfterreadingtheproblemIwoulddrawthefollowingpicture:

    wherehistheheight,whatIwanttofind.Iknowanangle,soIknowIneedtouseatrigonometricratiotosolvethisproblem.IamlookingforthesideoppositethegivenangleandIknowthehypotenuse.LookingatmydefinitionsIseeIshouldusethesineratiotowritetheunknownintermsofknowns.

    SoIhave

    or .

    Sousingmycalculatortocomputesin Ifindthekiteisapproximately61metersabovetheground.

    4.TheBrook'sareinstallingawidescreentelevisionwitha60inchdiagonal.Theirentertainmentcenteris48incheswideby36incheshigh,willthetelevisionfitintheircurrententertainmentcenter?

    AfterreadingtheproblemIdrawthefollowing:

    Iwanttofinddtoseeifthetelevisionwitha60inchdiagonalwillfitintoarectanglethatis48inchesby36inches.IcanusethePythagoreanTheoremtoputmyknownsintermsofmyunknown:

    or

    sothetelevisionwillfitexactly.

    5.Asurveyoris100metersfromthebaseofadam.Theangleofelevationtothetopofthedammeasures .Thesurveyor'seyelevelis1.73metersabovetheground.Findtheheightofthedamtothenearesthundredthofameter.

  • 1/7/2016 RightTriangleApplicationProblemsSolved

    http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/Applicationps.html 3/3

    AfterreadingtheproblemIdraw:

    Sothetopofthedamwillbedistanced+1.73m.Ihaveandangle,andthesideadjacenttotheangleandIamlookingforthesideoppositetheangle.Since

    Iwillusethistrigonometric

    ratiotosolveford.

    Iget:

    Iamnotquitedone,ImustaddthedistancethetriangleisabovethegroundtogettheheightIamlookingfor.Theheightofthedamis48.77m+1.73m=50.50m.

    Return

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