Trigonometric Ratios in Right Triangles

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Trigonometric Ratios in Right Triangles

• M. Bruley

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Trigonometric Ratios are based on the Concept of
Similar Triangles!
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All 45º- 45º- 90º Triangles are Similar!
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All 30º- 60º- 90º Triangles are Similar!
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2
1
½
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All 30º- 60º- 90º Triangles are Similar!
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60º
2
60º
5
1
30º
30º
1
60º
30º
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The Tangent Ratio
c a
?
?
b
If two triangles are similar, then it is also
true that
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Naming Sides of Right Triangles
Hypotenuse
q
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The Tangent Ratio
There are a total of six ratios that can be
made with the three sides. Each has a specific
name.
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The Six Trigonometric Ratios(The SOHCAHTOA model)
S O H C A H T O A
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The Six Trigonometric Ratios
The Cosecant, Secant, and Cotangent of q are the
Reciprocals of the Sine, Cosine,and Tangent of q.
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Solving a Problem withthe Tangent Ratio
We know the angle and the side adjacent to 60º.
We want to know the opposite side. Use
the tangent ratio
h ?
60º
53 ft
Why?
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Cofunctions p. 287
There are three pairs of cofunctions The sine
and the cosine The secant and the cosecant The
tangent and the cotangent
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Acknowledgements

• This presentation was made possible by training
  and equipment provided by an Access to Technology
  grant from Merced College.
• Thank you to Marguerite Smith for the model.
• Textbooks consulted were
• Trigonometry Fourth Edition by Larson Hostetler
• Analytic Trigonometry with Applications Seventh
  Edition by Barnett, Ziegler Byleen