# Right Triangle Trigonometry Solving Right Triangles

Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College Click one of the buttons below or press the enter key 2002 East Los Angeles College. All rights reserved. BACK NEXT EXIT Consider a Right Triangle. Note a is the leg opposite c is the leg opposite our right angle b is the leg adjacent to BACK NEXT EXIT

So that we have the following right triangle. BACK NEXT EXIT The six trigonometric ratios are defined as follows: opp sin ( ) = hyp adj cos ( ) = hyp opp tan ( ) = adj hyp ; csc ( ) = opp hyp ; sec ( ) = adj adj ; cot ( ) =

opp BACK NEXT EXIT What are the six trigonometric ratios for ? Note We need the length of one of the legs of our right triangle. BACK NEXT EXIT Use the Pythagorean Theorem . . . 2 2 3 ? 5 2 2

9 ? 25 2 ? 16 ; ? 4 ; ? 4 BACK NEXT EXIT For this triangle we get: hyp adj sin( ) 4 ; csc( ) 5 5 4

opp 3 5 cos( ) ; sec( ) 5 3 4 3 tan( ) ; cot( ) 3 4 BACK NEXT EXIT Notice we have another angle at . BACK NEXT EXIT We can obtain the six trigonometric ratios for ,

hyp HYP opp sin( ) 3 ; csc( ) 5 5 3 adj 4 5 cos( ) ; sec( ) 5 4 3 4 tan( ) ; cot( ) 4

3 BACK NEXT EXIT Together the model looks as follows. hyp HYP opp / adj adj / opp With + = 90 BACK NEXT EXIT Recall the 45 - 45 - 90 Special Triangle. What are the six trigonometric ratios for 45?

BACK NEXT EXIT hyp opp 45 adj 45 adj sin(45 ) hyp cos(45 ) tan(45 ) adj hyp

opp adj ; x x 2 ; ; x x 2 x x ; ; 1 2 1 2 ; ; 2

2 2 2 ; 1 BACK NEXT EXIT hyp opp 45 adj 45 csc(45 ) 2 sec(45 ) 2 cot(45 ) 1 BACK NEXT

EXIT Recall the 30 - 60 - 90 special triangle. What are the six trigonometric ratios for 30 ? What are the six trigonometric ratios for 60 ? BACK NEXT EXIT For 60 hyp opp 60 / adj 30 opp 30 / adj 60 sin(60 ) opp

hyp cos(60 ) tan(60 ) adj hyp opp adj ; x 3 ; ; ; 2x x 2x ; x 3

x 3 2 1 2 ; 3 BACK NEXT EXIT Thus, hyp opp 60 / adj 30 opp 30 / adj 60 csc(60 ) 2 3

; 2 3 3 sec(60 ) 2 cot(60 ) 1 3 ; 3 3 BACK NEXT EXIT For 30

hyp opp 60 / adj 30 opp 30 / adj 60 sin(30 ) cos(30 ) tan(30 ) opp adj opp ; hyp adj hyp ;

; x 2x x 3 x x 3 2x ; 1 2 ; ; 1 3 3 2 ;

BACK 3 3 NEXT EXIT Thus, hyp opp 60 / adj 30 opp 30 / adj 60 csc(30 ) 2 sec(30 ) cot(30 ) 2 3 3

3 ; 2 3 3 ; 3 BACK NEXT EXIT Summary sin() cos() tan() 30 12 3 2 3 3 45

2 2 2 2 1 60 3 2 12 3 BACK NEXT EXIT End of Right Triangle Trigonometry Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA 91754 Phone: (323) 265-8784 Email Us At:

[email protected] Our Website: http://www.matematicamente.org BACK NEXT EXIT

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