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Name___________________________‌ ‌
‌Performance‌‌Task‌‌Activity:‌‌Trig‌‌Review‌ ‌
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Task:‌ ‌Investigation:‌‌Oblique‌‌Triangles‌ ‌
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In‌‌this‌‌investigation‌‌you’ll‌‌explore‌‌a‌‌special‌‌relationship‌‌between‌‌the‌‌sines‌‌of‌‌the‌‌angle‌‌measures‌‌of‌‌
an‌‌oblique‌‌triangle‌‌and‌‌the‌‌lengths‌‌of‌‌the‌‌sides.‌ ‌
a) Draw‌‌at‌‌an‌‌acute‌‌triangle‌‌∆A
‌ BC‌‌and‌l‌abel‌‌the‌‌length‌‌of‌‌the‌‌side‌‌opposite‌‌<A
‌ ‌a‌ s‌a‌ ,‌t‌ he‌‌length‌‌of‌‌the‌‌side‌‌
opposite‌‌<B
‌ ‌a‌ s‌b‌ ,‌a‌ nd‌‌the‌‌length‌‌of‌‌the‌‌side‌‌opposite‌‌<C
‌ ‌a‌ s‌c‌ .‌D
‌ raw‌‌the‌‌altitude‌‌from‌‌<A
‌ ‌t‌ o‌‌BC ‌‌.‌L
‌ abel‌‌the‌‌
height‌h
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b) The‌‌altitude‌‌divides‌‌the‌‌original‌‌triangle‌‌into‌‌two‌‌right‌‌triangles,‌‌one‌‌containing‌‌<B
‌ ‌a‌ nd‌‌the‌‌other‌‌
containing‌‌<C
‌ .‌U
‌ se‌‌your‌‌knowledge‌‌of‌‌right‌‌triangle‌‌trigonometry‌‌to‌‌write‌‌an‌‌expression‌‌involving‌‌sin‌B
‌ ‌‌
and‌h
‌ ,‌a‌ nd‌‌an‌‌expression‌‌with‌‌sin‌C
‌ ‌a‌ nd‌h
‌ .‌C
‌ ombine‌‌the‌‌two‌‌expressions‌‌by‌‌eliminating‌h
‌ .‌W
‌ rite‌‌your‌‌new‌‌
expression‌‌as‌‌a‌‌proportion‌‌in‌‌the‌‌form‌ ‌
sinC
‌sinB
? = ? .‌ ‌
c) Now‌‌draw‌‌the‌‌altitude‌‌from‌‌<B
‌ ‌t‌ o‌‌AC ‌a‌ nd‌‌label‌‌the‌‌height‌j‌.‌R
‌ epeat‌‌Step‌‌2‌‌using‌‌expressions‌‌involving‌j‌,‌‌
sin‌C
‌ ,‌a‌ nd‌‌sin‌A
‌ .‌W
‌ hat‌‌proportion‌‌do‌‌you‌‌get‌‌when‌‌you‌‌eliminate‌j‌?‌ ‌
d) Compare‌‌the‌‌proportions‌‌that‌‌you‌‌wrote‌‌in‌‌Steps‌‌2‌‌and‌‌3.‌‌Use‌‌the‌‌transitive‌‌property‌‌of‌‌equality‌‌to‌‌
combine‌‌them‌‌into‌‌an‌‌extended‌‌proportion:‌ ?? = ?? = ?? . ‌
e) Using‌‌the‌‌formula‌‌from‌‌part‌‌d,‌‌solve‌‌this‌‌problem:‌ ‌
Towers‌‌A,‌‌B,‌‌and‌‌C‌‌are‌‌located‌‌in‌‌a‌‌national‌‌forest.‌‌From‌‌Tower‌‌B,‌‌the‌‌angle‌‌between‌‌Towers‌‌A‌‌and‌‌C‌‌is‌‌53.3°,‌‌
and‌‌from‌‌Tower‌‌C‌‌the‌‌angle‌‌between‌‌Towers‌‌A‌‌and‌‌B‌‌is‌‌46.7°.‌‌The‌‌distance‌‌between‌‌Towers‌‌A‌‌and‌‌B‌‌is‌‌4084‌‌m.‌‌
A‌‌lake‌‌between‌‌Towers‌‌A‌‌and‌‌C‌‌makes‌‌it‌‌difficult‌‌to‌‌measure‌‌the‌‌distance‌‌between‌‌them‌‌directly.‌‌What‌‌is‌‌the‌‌
distance‌‌between‌‌Towers‌‌A‌‌and‌‌C?‌ ‌
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