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The Sine Rule. A B C ao bo co

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**Finding The Sine Rule. Consider the triangle below: C A B ao bo co H**

Add the altitude line as shown. H is the height of the triangle. Now write the sine ratio for each right angled triangle: H = A sin bo H = B sin ao Look at these two results and try to work out the next line:

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C A B ao bo co H = A sin bo B sin ao A sin bo = B sin ao Now divide both sides by sin bo and sin ao . By changing the letters around we can prove that: The Sine Rule.

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**Calculating Sides Using The Sine Rule.**

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

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Example 2 Find the length of L in this triangle. 10m 133o 37o L Match up corresponding sides and angles: Now cross multiply. Solve for L. = 12.14m

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

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**Calculating Angles Using The Sine Rule.**

Example 1. ao 45m 23o 38m Find the angle ao Match up corresponding sides and angles: Now cross multiply: Solve for sin ao = 0.463 Use sin to find ao

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Example 2. 143o 75m 38m bo Find the size of the angle bo Match up corresponding sides and angles: Cross multiply. Solve for sinbo = 0.305 Use sin to find bo

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**What Goes In The Box ? 2 Calculate the unknown angle in the following:**

(2) 14.7cm bo 14o 12.9cm (1) 14.5m 8.9m ao 100o ao = 37.2o (3) 93o 64mm co 49mm bo = 16o c =49.9o

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There are three ratios that you need to learn: Where are the hypotenuse, adjacent and opposite lengths. This is opposite the right-angle This is next to.

There are three ratios that you need to learn: Where are the hypotenuse, adjacent and opposite lengths. This is opposite the right-angle This is next to.

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