Transcript Rewriting Equations & Formulas

Same Shape Triangles
Teacher Page – the complete lesson is available
at the page Teaching Trigonometry.
http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teachi
ng/trig.htm
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Same Shape Ratios
TG.4 Special Ratios of Right Triangles
10/29/14
This work by Southwest Washington Mathematics Common Core Consortium is licensed
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under a Creative Commons Attribution 4.0 International License.
Practice Target
• Practice 6. Attend to precision.
• Practice 7. Look for and make use
of structure.
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Learning Target
G-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.
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Launch
Which side of ΔABC is the hypotenuse?
hypotenuse
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Launch
Which side is opposite from angle B?
opposite
hypotenuse
6
Launch
Referring to angle B, what name would
you give to side AC?
opposite
hypotenuse
adjacent
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Launch
Referring to angle C, which side is the hypotenuse
 AB
 BC
 AC
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Always, Sometimes, Never
In all triangles,
• there is one
hypotenuse.
• hypotenuse is opposite
angle A.
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Always, Sometimes, Never
In any right triangle,
• the hypotenuse is the
longest side
• the smallest side is
opposite the smallest
angle
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Always, Sometimes, Never
In 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
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Explore
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Calculating ratios for similar triangles
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Calculating ratios for similar triangles
• 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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Record our Ratios
𝜃
(degrees)
20
30
40
45
50
60
70
opp
hyp
adj
hyp
opp
adj
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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.
1
2
3
4
5
Rate your understanding of the
target from 1 to 5.
5 is a bullseye!
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Practice
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Ticket Out
Find the ratios for
angle M
opp

hyp
adj

hyp
opp

adj
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Ticket Out
Find the ratios for
angle M
opp 2.8

hyp 4.9
adj
4

hyp 4.9
opp 2.8

adj
4
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