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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 BACKNEXT Click one of the buttons below or press the enter key © 2002 East Los Angeles College. All rights reserved.

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Consider a Right Triangle. Note – a is the leg opposite c is the leg opposite our right angle b is the leg adjacent to EXIT BACKNEXT

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So that we have the following right triangle. EXIT BACKNEXT

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The six trigonometric ratios are defined as follows: EXIT BACKNEXT

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What are the six trigonometric ratios for ? Note – We need the length of one of the legs of our right triangle. EXIT BACKNEXT

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Use the Pythagorean Theorem... EXIT BACKNEXT

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For this triangle we get: hyp adj opp EXIT BACKNEXT

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Notice we have another angle at . EXIT BACKNEXT

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We can obtain the six trigonometric ratios for , HYP opp adj hyp EXIT BACKNEXT

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Together the model looks as follows. HYP adj / opp opp / adj hyp With + = 90° EXIT BACKNEXT

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Recall the 45º - 45º - 90º Special Triangle. What are the six trigonometric ratios for 45º? EXIT BACKNEXT

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hyp opp 45º adj 45º EXIT BACKNEXT

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hyp opp 45º adj 45º EXIT BACKNEXT

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Recall the 30º - 60º - 90º special triangle. What are the six trigonometric ratios for 30 º ? What are the six trigonometric ratios for 60 º ? EXIT BACKNEXT

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For 60º hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

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Thus, hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

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For 30º hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

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Thus, hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

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Summary sin( )cos( )tan( ) 30º 45º1 60º EXIT BACKNEXT

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End of Right Triangle Trigonometry Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA Phone: (323) Us At: Our Website: EXIT BACKNEXT

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