1. Sin and Cosine Rules Objectives: calculate missing sides and angles is non-right angles triangles

2. Labelling The Triangle B A C a b c Vertices (corners) are usually labelled with capital letters, Sides are usually labelled with small letters. Note: Angle A is opposite side a Angle B is opposite side b Angle C is opposite side c

3. The Sin Rules OR Flip it upside down A B C c a b

4. Applying the sin rule 5 cm 8 cm 38 0 x Find angle x A B C a b c 1. Make sure your sides are labelled. 2. Decide whether you are looking for an angle or side and use the appropriate equation or To find an angle 3. Identify the information you have and what part of the equation to use,

5. Applying the formula 5 cm 8 cm 38 0 x A B C a b c Sin x 8 Sin 38 5 = Sin x = 0.123…. 8 Sin x = 0.123 x 8 = 0.985 x = 80.1 0

6. Example 2: Using the sin rule A B C a b c 42 0 28 0 9 m x Calculate length x Looking for length Insert values into equation x = sin 42 x 19.17 x = 12.83 m to 2 dp.

7. The Cosine Rule b 2 = a 2 + c 2 - 2acCosB In its most usual form: To find a side: To find an angle: A B C c a b

8. Rearranging The Formula To find any side: b 2 = a 2 + c 2 - 2acCosB a 2 = b 2 + c 2 - 2bcCosA c 2 = a 2 + b 2 - 2abCosC or To find any angle:

9. Using the formula B A C c a b 5 cm 40 0 3.2 cm Calculate length p p Make sure your triangle is labelled Choose the correct equation to use: b 2 = a 2 + c 2 - 2acCosBa 2 = b 2 + c 2 - 2bcCosA c 2 = a 2 + b 2 - 2abCosC For sides : For angles : For side b

10. Substituting into the formula B A C 5 cm 40 0 3.2 cm p c a b b 2 = a 2 + c 2 - 2acCosB b 2 = 5 2 + 3.2 2 - 2x5x3.2Cos40 b 2 = 35.24 - 32Cos40 b 2 = 10.73 (2dp) b = 3.3 (1dp)

11. Example 2. Calculate angle s 8 cm 12 cm 7 cm s A B C c a b Cos C = 0.828…. (3 dp) C = 34.1 0 (1 dp)