L1 Relating Side Length and Angles
Completion requirements
Unit A: Geometry
Chapter 3: Trigonometry
Determining the Relationship between Side Length and Angles in a Triangle
When labelling a triangle, angles are labelled with capital letters and sides are labelled with lowercase letters. The angle and the side across it share the same letter name—these are called matching pairs.
Find the matching pairs of sides and opposite angles in ΔABC.
The side labelled 64 cm is named side a since it is opposite (across) from «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»A«/mi» «/math». The 64 cm side and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»A«/mi» «/math» are a matching pair.
The side labelled 83 cm is named side b since it is opposite (across) from «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»B«/mi» «/math». The 83 cm side and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»B«/mi» «/math» are a matching pair.
The side labelled 52 cm is named side c. The angle opposite this side is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»C«/mi» «/math». The 52 cm side and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»C«/mi» «/math» are a matching pair.
a.
Which side is opposite
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»
«mo»§#8736;«/mo»
«mi»A«/mi»
«/math»?
b.
Which side is opposite
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»
«mo»§#8736;«/mo»
«mi»B«/mi»
«/math»?
c.
Which angle is opposite to the 52 cm side?
a.
The side labelled 64 cm is named side a since it is opposite (across) from «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»A«/mi» «/math». The 64 cm side and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»A«/mi» «/math» are a matching pair.
b.
The side labelled 83 cm is named side b since it is opposite (across) from «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»B«/mi» «/math». The 83 cm side and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»B«/mi» «/math» are a matching pair.
c.
The side labelled 52 cm is named side c. The angle opposite this side is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»C«/mi» «/math». The 52 cm side and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8736;«/mo» «mi»C«/mi» «/math» are a matching pair.