The Cosine Rule Can be used with ANY triangle, NOT just with right triangles!!!

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Presentation transcript:

The Cosine Rule Can be used with ANY triangle, NOT just with right triangles!!!

What do you have to know to use the Cosine Rule? Two sides and the included angle (SAS) C A B c a b BB AA CC

What do you have to know to use the Cosine Rule? OR all three sides (SSS) C B c a b BB AA CC

The Cosine Rule is: C B c a b BB AA CC

IN OTHER WORDS: (One side) 2 = (other side) 2 +(last side) 2 - 2(other side)(last side)cos(angle of 1 st side)

Find the remaining sides and angles in the triangle using the Cosine Rule What are we given? 2 sides and the included angle – SAS: c, b, A  Label sides and angles a b c BB CC AA

Find the remaining sides and angles in the triangle using the Cosine Rule Let’s find side ‘a’ first a b c BB CC AA Which version of the Cosine Rule do we want to use? ( ) 2 =( ) 2 +( ) 2 -2( )( )cos( ) a b c b c AA

Find the remaining sides and angles in the triangle using the Cosine Rule a b c BB CC AA Plug in and Solve: ( ) 2 =( ) 2 +( ) 2 -2( )( )cos( ) a  a=8.80cm 8.80 cm

Find the remaining sides and angles in the triangle using the Cosine Rule a b c BB CC AA What do we have now? 3 sides – SSS: a,b,c What do we still need to find? B  and C 

Find the remaining sides and angles in the triangle using the Cosine Rule Let’s find side B  next a b c BB CC AA Which version of the Cosine Rule do we want to use? ( ) 2 =( ) 2 +( ) 2 -2( )( )cos( ) b a c a c BB 8.80 cm

Find the remaining sides and angles in the triangle using the Cosine Rule a b c BB CC AA Plug in and Solve: ( ) 2 =( ) 2 +( ) 2 -2( )( )cos( ) BB B  =81.3  8.80 cm 13

Find the remaining sides and angles in the triangle using the Cosine Rule Finally let’s find side C  a b c BB CC AA Which version of the Cosine Rule do we want to use? ( ) 2 =( ) 2 +( ) 2 -2( )( )cos( ) c a b a b CC 8.80 cm

Find the remaining sides and angles in the triangle using the Cosine Rule a b c BB CC AA Plug in and Solve: ( ) 2 =( ) 2 +( ) 2 -2( )( )cos( ) CC C  =56.8  8.80 cm 11

YOU DO: Find the remaining sides and angles of the triangle using the Cosine Rule.