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