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Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACK NEXT Click one of the buttons below or press the enter key © 2002 East Los Angeles College. All rights reserved.

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Page 1: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Right Triangle TrigonometrySolving Right Triangles

Prepared by Title V Staff:Daniel Judge, Instructor

Ken Saita, Program Specialist

East Los Angeles College

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© 2002 East Los Angeles College. All rights reserved.

Page 2: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Consider a Right Triangle.

Note – a is the leg opposite c is the leg opposite our right angle b is the leg adjacent to

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Page 3: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

So that we have the following right triangle.

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Page 4: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

The six trigonometric ratios are defined as follows:

opp hypsin ( ) = ; csc ( ) =

hyp opp

adj hypcos ( ) = ; sec ( ) =

hyp adj

opp adj tan ( ) = ; cot ( ) =

adj opp

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Page 5: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

What are the six trigonometric ratios for ?

Note – We need the length of one of the legs of our right triangle.

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Page 6: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Use the Pythagorean Theorem . . .

2 2 23 ? 5

29 ? 25

2? 16 ; ? 4 ; ? 4

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Page 7: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

For this triangle we get:

hyp

adj

opp

4 5sin( ) csc( )

5 4

3 5cos( ) ; sec( )

5 3

4 3tan( ) ; cot( )

3 4

;

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Page 8: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Notice we have another angle at .

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Page 9: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

We can obtain the six trigonometric ratios for ,

HYP

opp

adj

3 5sin( ) ; csc( )

5 3

4 5cos( ) ; sec( )

5 4

3 4tan( ) ; cot( )

4 3

hyp

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Page 10: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Together the model looks as follows.

HYP

adj / opp

opp / adj hyp

With + = 90°

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Page 11: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Recall the 45º - 45º - 90º Special Triangle.

What are the six trigonometric ratios for 45º?

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Page 12: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

hypopp 45º

adj 45º

adj x 1 2sin(45 ) ; ; ;

hyp 2x 2 2

adj x 1 2cos(45 ) ; ; ;

hyp 2x 2 2

opp xtan(45 ) ; ; 1

adj x

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Page 13: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

hypopp 45º

adj 45º

2csc(45 )

2sec(45 )

cot(45 ) 1

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Page 14: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Recall the 30º - 60º - 90º special triangle.

What are the six trigonometric ratios for 30º ?What are the six trigonometric ratios for 60º ?

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Page 15: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

For 60º hyp

opp 60º / adj 30º

opp 30º / adj 60º

opp x 3 3sin(60 ) ; ;

hyp 2x 2

adj x 1cos(60 ) ; ;

hyp 2x 2

opp x 3tan(60 ) ; ; 3

adj x

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Page 16: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Thus, hyp

opp 60º / adj 30º

opp 30º / adj 60º

2 2 3csc(60 ) ;

33

sec(60 ) 2

1 3cot(60 ) ;

33

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Page 17: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

For 30º hyp

opp 60º / adj 30º

opp 30º / adj 60º

opp x 1sin(30 ) ; ;

hyp 2x 2

adj x 3 3cos(30 ) ; ;

hyp 2x 2

opp x 1 3tan(30 ) ; ; ;

adj x 3 3 3

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Page 18: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Thus, hyp

opp 60º / adj 30º

opp 30º / adj 60º

csc(30 ) 2

3cot(30 ) ; 3

3

2 2 3sec(30 ) ;

33

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Page 19: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

Summary

sin() cos() tan()

30º

45º 1

60º

1 2

2 2

3 2

3 2

2 2

1 2

3 3

3

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Page 20: Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles

End of Right Triangle Trigonometry

Title V East Los Angeles College

1301 Avenida Cesar ChavezMonterey Park, CA 91754

Phone: (323) 265-8784

Email Us At:[email protected]

Our Website:http://www.matematicamente.org

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