S4_3_Sine_Cosine_Ch12

S4_3_Sine_Cosine_Ch12 - Trigonometry S4 Credit Sine Rule...

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13 Feb 2012 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Created by Mr. Lafferty Maths Dept. Trigonometry Trigonometry www.mathsrevision.com Cosine Rule Finding a Length Sine Rule Finding a length Mixed Problems S4 Credit Sine Rule Finding an Angle Cosine Rule Finding an Angle Area of ANY Triangle

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13 Feb 2012 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 2 1.   Mult iply out t h e  b r ac ke t s and s im plif y                        5 (y - 5 ) - 7 (5 - y)  2 .   T r ue  or  f als e  t h e  gr ad ie nt of t h e  line  is  5 3         y = 5 x -  4 3 .   Fac t or is e  x - 10 0   S4 Credit
13 Feb 2012 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Learning Intention Success Criteria Success Criteria 1. 1. Know how to use the sine rule to solve  Know how to use the sine rule to solve  REAL LIFE problems involving  REAL LIFE problems involving  lengths. lengths. 1.   To show how to use the sine rule to  solve REAL LIFE problems  involving finding  the  length of a  side of a triangle . Sine Rule Sine Rule S4 Credit

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C B A 13 Feb 2012 13 Feb 2012 Created by Mr Lafferty Maths Dept Created by Mr Lafferty Maths Dept Sine Rule Sine Rule www.mathsrevision.com S4 Credit a b c The Sine Rule can be used with ANY triangle  as long as we have been given enough information. Works for any Triangle a b c = = S inA S inB S inC
Deriving the rule B C A b c a Consider a general triangle ABC. The Sine Rule Draw CP perpendicular to BA P CP SinB aSinB a = =   also SinA bSinA b = = = b SinA = a b = This can be extended to  a b c SinC = = or equivalently a b c = =

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Calculating Sides Calculating Sides Using The Sine Rule Using The Sine Rule 10m 34 o 41 o a Match up corresponding sides and angles: sin 41 o a = 10 sin 34 o Rearrange and solve for  a . 10sin 41 sin 34 o o a = 10 0.656 11.74 0.559 a m = = Example 1 : Find the length of  a  in this triangle. www.mathsrevision.com S4 Credit A B C sin sin sin o a b c A B C = =
Calculating Sides Calculating Sides Using The Sine Rule Using The Sine Rule www.mathsrevision.com S4 Credit 10m 133 o 37 o d sin133 o d = 10 sin 37 o 10sin133 sin 37 o o d = 10 0.731 0.602 d = = 12.14m Match up corresponding sides and angles: Rearrange and solve for  d . Example 2 : Find the length of  d  in this triangle. C D E sin sin sin o c d e C D E = =

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What goes in the Box ? What goes in the Box ? Find the unknown side in each of the triangles below: (1) 12cm 72 o 32 o a (2) 93 o b 47 o 16mm A = 6.7cm B = 21.8mm www.mathsrevision.com S4 Credit 13 Feb 2012 13 Feb 2012 Created by Mr Lafferty Maths Dept Created by Mr Lafferty Maths Dept
13 Feb 2012 13 Feb 2012 Created by Mr. Lafferty Maths Dept.

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This note was uploaded on 02/13/2012 for the course MATH 115 115 taught by Professor Jones during the Spring '10 term at University of Phoenix.

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S4_3_Sine_Cosine_Ch12 - Trigonometry S4 Credit Sine Rule...

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