2Finding 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 boH =B sin aoLook at these two results and try to work out the next line:
3CABaobocoH =A sin boB sin aoA sin bo = B sin aoNow divide both sides by sin bo and sin ao .By changing the letters around we can prove that:The Sine Rule.
4Calculating Sides Using The Sine Rule. Example 1Find the length of L in this triangle.10m34o41oLMatch up corresponding sides and angles:Now cross multiply.Solve for L.
5Example 2Find the length of L in this triangle.10m133o37oLMatch up corresponding sides and angles:Now cross multiply.Solve for L.= 12.14m
6What Goes in the Box ? 1Find the unknown side in each of the triangles below:(1)12cm72o32oAB = 21.8mm(2)93oB47o16mmA = 6.7cm(4)143oD12o17m(3)87o89m35oCC = 51.12mD = 49.21m
7Calculating Angles Using The Sine Rule. Example 1.ao45m23o38mFind the angle aoMatch up corresponding sides and angles:Now cross multiply:Solve for sin ao= 0.463Use sin to find ao
8Example 2.143o75m38mboFind the size of the angle boMatch up corresponding sides and angles:Cross multiply.Solve for sinbo= 0.305Use sin to find bo
9What Goes In The Box ? 2 Calculate the unknown angle in the following: (2)14.7cmbo14o12.9cm(1)14.5m8.9mao100oao = 37.2o(3)93o64mmco49mmbo = 16oc =49.9o