UsingLawsofSinesandCosines Date________________
SolveeachoftheproblemsbelowusingtheLawofSinesorLawofCosinesif
needed.
1.Thelidofagrandpianoisproppedopenbyasupportingarmasshowninthediagram.
Kieranknowsthesupportingarmis2feetlongandmakesa60°anglewiththepiano.He
alsoknowsthelidmakesa23°anglewiththepiano.Howwideisthepiano?
2.WeknowthattheLawofCosinescanbeexpressedas:
𝑐 ! = 𝑎 ! + 𝑏 ! − 2 ∙ 𝑎 ∙ 𝑏 ∙ cos (𝐶)
Provethatthisisequivalenttotheequation:
cos 𝐶 =
! ! !! ! !! !
!!∙!∙!
3.Find𝑚∠𝐴tothenearestdegree.{Hint–useLawofSinestwice}
4.StatewhethertheLawofSinesortheLawofCosinesisthebestchoicetosolveforthe
unknownvaluexineachtriangle.Youdonotneedtosolveforxintheseproblems.
a) b)
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c)
d)
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5.Adangerouscriminalisontheloose.Thepolicebelievethecriminalishiding
somewherebetweencitiesA,B,andC.AmanhuntwasorganizedstartingatCityA.
Thedistancesbetweenthecitiesareasfollows:𝐴𝐵 = 18 𝑚𝑖, 𝐵𝐶 = 15 𝑚𝑖 & 𝐴𝐶 = 25 𝑚𝑖.
Whatarethethreeanglesthatmakeupthesearchtriangle?
𝑚∠𝐴 = _____________,𝑚∠𝐵 = _____________,𝑚∠𝐶 = _____________