SECONDARY MATH II // MODULE 6
SIMILARITY & RIGHT TRIANGLE TRIGONOMETRY – 6.8
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
6. 8 Are Relationships Predictable?
A Develop Understanding Task
Inyournotebookdrawarighttrianglewithoneangleof60°.Measureeachsideofyourtriangleasaccuratelyasyoucanwithacentimeterruler.Usingthe600angleastheangleofreferencelistthemeasureforeachofthefollowing: Lengthoftheadjacentside: Lengthoftheoppositeside: Lengthofthehypotenuse:Createthefollowingratiosusingyourmeasurements:
opposite sidehypotenuse
= adjacent sidehypotenuse
=
opposite sideadjacent side
=
1. Compareyourratioswithothersthathadatriangleofadifferentsize.Whatdoyounotice?Explainanyconnectionsyoufindtoothers’work?
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SECONDARY MATH II // MODULE 6
SIMILARITY & RIGHT TRIANGLE TRIGONOMETRY – 6.8
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
2. Intherighttrianglesbelowfindthemissingsidelengthandthencreatethedesiredratiosbasedontheangleofreference(angleAandangleD).
ListtheratiosforΔABC usingangleAastheangleofreference.
ListtheratiosforΔDEF usingangleDastheangleofreference.
opposite sidehypotenuse
=
adjacent sidehypotenuse
=
opposite sideadjacent side
=
opposite sidehypotenuse
=
adjacent sidehypotenuse
=
opposite sideadjacent side
=
3. Whatdoyounoticeabouttheratiosfromthetwogiventriangles?Howdotheseratioscompareto
theratiosfromthetriangleyoumadeonthepreviouspage?
4. Whatcanyouinferabouttheanglemeasuresof∆!"# and ∆!"#?
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