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The Sine Rule. A B C aoao bobo coco

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Finding The Sine Rule. Consider the triangle below: C A B aoao bobo coco Add the altitude line as shown. H Now write the sine ratio for each right angled triangle: H =A sin b o H =B sin a o Look at these two results and try to work out the next line: H is the height of the triangle.

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C A B aoao bobo coco H =A sin b o H =B sin a o A sin b o = B sin a o Now divide both sides by sin b o and sin a o. By changing the letters around we can prove that: The Sine Rule.

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Calculating Sides Using The Sine Rule. 10m 34 o 41 o L Find the length of L in this triangle. Match up corresponding sides and angles: Now cross multiply. Solve for L. Example 1

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10m133 o 37 o L Find the length of L in this triangle. Match up corresponding sides and angles: Now cross multiply. Solve for L. = 12.14m Example 2

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What Goes in the Box ? 1 Find the unknown side in each of the triangles below: (1) 12cm 72 o 32 o A (2) 93 o B 47 o 16mm (3) 87 o 89m 35 o C (4) 143 o D 12 o 17m A = 6.7cm B = 21.8mm C = 51.12mD = 49.21m

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Calculating Angles Using The Sine Rule. Example 1. aoao 45m 23 o 38m Find the angle a o Match up corresponding sides and angles: Now cross multiply: Solve for sin a o = 0.463Use sin to find a o

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Example o 75m 38m bobo Find the size of the angle b o Match up corresponding sides and angles: Cross multiply. Solve for sinb o = 0.305Use sin to find b o

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What Goes In The Box ? 2 Calculate the unknown angle in the following: (1) 14.5m 8.9m aoao 100 o (2) 14.7cm bobo 14 o 12.9cm (3) 93 o 64mm coco 49mm a o = 37.2 o b o = 16 o c =49.9 o

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