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The Sine Rule.

A. b o. C. a o. c o. B. The Sine Rule. c o. B. A. a o. b o. C. Finding The Sine Rule. Consider the triangle below:. 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 b o. H =. B sin a o.

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The Sine Rule.

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  1. A bo C ao co B The Sine Rule.

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

  3. co B A H = A sin bo H = B sin ao ao bo C 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.

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

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

  6. 12cm B (1) (2) 47o 32o A 72o 93o 16mm 17m (4) (3) 143o C 89m 12o 87o 35o D What Goes in the Box ? 1 Find the unknown side in each of the triangles below: B = 21.8mm A = 6.7cm C = 51.12m D = 49.21m

  7. 45m 38m 23o ao Calculating Angles Using The Sine Rule. Example 1. Find the angle ao Match up corresponding sides and angles: Now cross multiply: Solve for sin ao = 0.463 Use sin-1 0.463 to find ao

  8. 75m bo 143o 38m Example 2. Find the size of the angle bo Match up corresponding sides and angles: Cross multiply. Solve for sinbo = 0.305 Use sin-1 0.305 to find bo

  9. (1) 8.9m 100o (2) ao 12.9cm bo 14.5m 14o (3) 93o 49mm 14.7cm co 64mm What Goes In The Box ? 2 Calculate the unknown angle in the following: ao = 37.2o bo = 16o c =49.9o

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