Post on 23-Dec-2015
Same Shape TrianglesTeacher Page – the complete lesson is available
at the page Teaching Trigonometry. http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm
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10/29/14
This work by Southwest Washington Mathematics Common Core Consortium is licensed under a Creative Commons Attribution 4.0 International License.
Same Shape Ratios
TG.4 Special Ratios of Right Triangles
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Practice Target• Practice 6. Attend to precision.
• Practice 7. Look for and make use of structure.
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Learning TargetG-SRTc I can define trigonometric ratios and
solve problems involving right triangles. Identify and define the sine, cosine and
tangent ratios in terms of the angles of the triangles.
Use similar triangles to justify trigonometric ratio.
Which side of ΔABC is the hypotenuse?
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Launch
hypotenuse
Which side is opposite from angle B?
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Launch
hypotenuseopposite
Referring to angle B, what name would you give to side AC?
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Launch
hypotenuseopposite
adjacent
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Launch
AB
BC
AC
hypotenuseReferring to angle C, which side is the
Always, Sometimes, NeverIn all triangles, • there is one
hypotenuse.• hypotenuse is opposite
angle A.
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Always, Sometimes, NeverIn any right triangle, • the hypotenuse is the
longest side• the smallest side is
opposite the smallest angle
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Always, Sometimes, NeverIn this triangle, • Angles B and C have the
same opposite side.• Angles B and C have the
same hypotenuse.• The side opposite angle
B is the side adjacent to angle C 11
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Explore
Calculating ratios for similar triangles
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You need 2 papersper team.
• Each student takes two triangles.
• Measure each side to the nearest tenths of a centimeter and enter in the worksheet.
• Write the ratios as fractions and use a calculator to estimate them to 3 decimal places.
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Calculating ratios for similar triangles
• Complete the worksheet including the mean values for each ratio to 2 decimal places.
• Stack your triangles as neatly as possible on top of each other and discuss their findings.
• All members of your team need to be prepared to share your ratios and your findings with the class.
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Calculating ratios for similar triangles
Record our Ratios
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𝜃(degrees) 20 30 40 45 50 60 70
opphyp
adjhyp
oppadj
Graph the three ratios from our table
• Use 3 different colors.
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Debrief• How are the patterns you
observe in the table shown in the graph?
• What information do you get from the graph, but not the table?
• What information do you get from the table, but not the graph?
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Learning Target Did you hit the target? Practice 7. Look for and make use of structure
.
Rate your understanding of the target from 1 to 5.
5 is a bullseye!
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Practice
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Ticket OutFind the ratios for
angle M
opphyp
=
adjhyp
=
oppadj
=
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Ticket OutFind the ratios for
angle M
opphyp
=2.84.9
adjhyp
=4
4.9oppadj
=2.84