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The Sine Rule C. McMinn. SOH/CAH/TOA can only be used for right-angled triangles. The Sine Rule can be used for any triangle: AB C a b c The sides are.

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Presentation on theme: "The Sine Rule C. McMinn. SOH/CAH/TOA can only be used for right-angled triangles. The Sine Rule can be used for any triangle: AB C a b c The sides are."— Presentation transcript:

1 The Sine Rule C. McMinn

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

3 Example 1: C B A 76 º 7cm Find the length of BC x a sinA c sinC b c a = x sin76º 7 sin63 º =× sin76ºsin76º × x = 7 sin63º × sin76º x = 7.6 cm 63 º Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.

4 Example 2: Q R P 55 º 82 º 15cm Find the length of PR x p sinP q sinQ rq p = 15 sin82º x sin43 º =× sin43ºsin43º × = x 15 sin82º sin43º × x = cm 43 º Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.

5 A B C D E F G H I P Q R 62 º 53 º 5 cm x 28 º 130 º 13 cm x 41 º 76 º x 26 mm 37 º 77 º 10 m x 5.2 cm 57 º x 62 º x 86 º 35 º 12 cm x 85 º 65 º 6 km º º 61 º

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

7 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! sinA a sinB b sinC c= Alternative form of the Sine Rule:

8 Example 1: A B C 72 º 6cm Find the size of angle ABC x º sinA a sinB b b a c = sin72º 6 sin xº 4 =× 44 ×4 × = sin xº 4 ×4 × sin xº = Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use. 4cm sin72º 6 x = sin = 39.3º

9 Example 2: R Q P 85 º 8.2cm Find the size of angle PRQ x º sinP p sinR r q r p = sin85º 8.2 sin xº 7 =× 77 ×7 × = sin xº 7 ×7 × sin xº = cm sin85º 8.2 x = sin = 58.3º

10 º 6 cm xºxº 5 cm xºxº 105 º 8.8 cm 6.5cm xºxº 33 º 5.2 cm 5.5 cm xºxº 7.6 cm 8.2 cm xºxº 82 º 8 m 70 º 9.5 m (Be careful!) xºxº 27 º 6 km 3.5 km 74 º xºxº 7 mm 9 mm º 22.9 º

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


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