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The Sine Rule

The Sine Rule. C. McMinn. a sin A. b sin B. c sin C. = =. SOH/CAH/TOA can only be used for right-angled triangles. The Sine Rule can be used for any triangle:. C. b. The sides are labelled to match their opposite angles. a. A. B. c. The Sine Rule:. A. Example 1 :.

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The Sine Rule

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  1. The Sine Rule C. McMinn

  2. a sinA b sinB c sinC = = SOH/CAH/TOA can only be used for right-angled triangles. The Sine Rule can be used for any triangle: C b The sides are labelled to match their opposite angles a A B c The Sine Rule:

  3. A Example 1: Find the length of BC 76º c 7cm b 63º C x B a a sinA c sinC = Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use. x sin76º 7 sin63º sin76º × = × sin76º 7 sin63º x = ×sin76º x = 7.6 cm

  4. P Example 2: Find the length of PR 82º x r q 43º 55º Q 15cm R p p sinP q sinQ = Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use. 15 sin82º x sin43º sin43º × = × sin43º 15 sin82º = x sin43º × x = 10.33 cm

  5. G B 3. 1. 2. F 53º 13 cm 41º x 8.0 35.3 5.5 x 62º A x 130º 28º D E 5 cm 63º 76º C H 26 mm I 10.7 4. 5.2 cm 5. x 61º R 6. P 37º 66º 57º 10 m 35º x 5.2 77º 62º Q 12 cm 6 km 85º 7. x 6.6 65º 86º x 6.9

  6. Remember: • Draw a diagram • Label the sides • Set out your working exactly as you have been shown • Check your answers regularlyand ask for help if you need it

  7. sinA a sinB b sinC c = = Finding an Angle The Sine Rule can also be used to find an angle, but it is easier to use if the rule is written upside-down! Alternative form of the Sine Rule:

  8. C Example 1: Find the size of angle ABC 6cm a 4cm b x º 72º A B c sinA a sinB b = Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use. sin72º 6 sin xº 4 4× = × 4 sin72º 6 = sin xº 4× sin xº = 0.634 x = sin-1 0.634 = 39.3º

  9. P Example 2: Find the size of angle PRQ 85º q 7cm r x º R p 8.2cm Q sinP p sinR r = sin85º 8.2 sin xº 7 7× = × 7 sin85º 8.2 = sin xº 7× sin xº = 0.850 x = sin-1 0.850 = 58.3º

  10. 7.6 cm 1. 2. 3. 82º 105º 6.5cm 47º 5 cm 8.2 cm 66.6° xº 37.6° xº 45.5° xº 8.8 cm 6 cm 5. 6 km 4. 5.5 cm 31.0° xº 27º 3.5 km 51.1° xº 5.2 cm 33º 7. 6. 8 m 74º 57.7° xº 70º 9 mm 9.5 m 92.1° xº 52.3º (←Be careful!→) 22.9º 7 mm

  11. Remember: • Draw a diagram • Label the sides • Set out your working exactly as you have been shown • Check your answers regularlyand ask for help if you need it

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