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Sin and Cosine Rules

Sin and Cosine Rules. Objectives: calculate missing sides and angles is non-right angles triangles. A. b. c. C. B. a. Labelling The Triangle. Note: Angle A is opposite side a Angle B is opposite side b Angle C is opposite side c.

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Sin and Cosine Rules

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

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

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

  4. Applying the sin rule B Find angle x a 8 cm 380 1. Make sure your sides are labelled. C c 2. Decide whether you are looking for an angle or side and use the appropriate equation 5 cm x b A or To find an angle 3. Identify the information you have and what part of the equation to use,

  5. Applying the formula B a 8 cm 380 C c 5 cm x Sin x Sin 38 b = A 8 5 Sin x = 0.123…. 8 Sin x = 0.123 x 8 = 0.985 x = 80.10

  6. Example 2: Using the sin rule A Calculate length x Looking for length c 9 m b x 420 Insert values into equation B a 280 C x = sin 42 x 19.17 x = 12.83 m to 2 dp.

  7. The Cosine Rule In its most usual form: b2 = a2 + c2 - 2acCosB To find a side: A To find an angle: c B b a C

  8. Rearranging The Formula • To find any side: b2 = a2 + c2 - 2acCosB or a2 = b2 + c2 - 2bcCosA or c2 = a2 + b2 - 2abCosC • To find any angle: or or

  9. A c b B a C Using the formula Calculate length p Make sure your triangle is labelled 3.2 cm p 400 5 cm Choose the correct equation to use: For side b For sides: c2 = a2 + b2 - 2abCosC a2 = b2 + c2 - 2bcCosA b2 = a2 + c2 - 2acCosB For angles:

  10. A c b B a C Substituting into the formula b2 = a2 + c2 - 2acCosB 3.2 cm b2 = 52 + 3.22 - 2x5x3.2Cos40 p 400 b2 = 35.24 - 32Cos40 5 cm b2 = 10.73 (2dp) b = 3.3 (1dp)

  11. Example 2. • Calculate angle s A 7 cm B c b 8 cm a 12 cm Cos C = 0.828…. (3 dp) s C = 34.10 (1 dp) C

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