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The Sine Rule قاعدة الجيب Wassim Al Meniem 1

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*To use the sine rule to find the side of a triangle. * To use the sine rule to find the angle of a triangle. L.I: S.C: write down the sine rule formula. Find the side and the angle using the sine rule. 2Wassim Al Meniem

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A B C 62 º 53 º 5 cm x H I 41 º 76 º x 26 mm º G º 6 cm xºxº 5 cm 8.2 cm xºxº 82 º Wassim Al Meniem

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The Sine Rule can be used for any triangle : تستخدم مع أي مثلث AB C a b c The sides are labelled to match their opposite angles a sinA b sinB c sinC= The Sine Rule: 4Wassim Al Meniem

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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 : 5Wassim Al Meniem

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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. ارسم مستقيم من الضلع للزاوية المقابلة له ليساعدك على التعويض بالقاعدة. 6Wassim Al Meniem

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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. 7Wassim Al Meniem

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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 66 º 63 º 61 º 8Wassim Al Meniem

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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 Wassim Al Meniem

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Remember:تذكر Draw a diagramارسم الشكل Label the sides سمّي الأضلاع Set out your working exactly as you have been shownاجعل عملك منسقا كالذي رأيته بالعرض التقديمي Check your answers regularly and ask for help if you need it تحقق من اجاباتك بشكل منتظم واسأل المدرس للمساعدة 10Wassim Al Meniem

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Finding an Angle إيجاد الزاوية The Sine Rule can also be used to find an angle, but it is easier to use if the rule is written upside-down! يمكن استخدام قاعدة الجيب لإيجاد الزاوية sinA a sinB b sinC c= Alternative form of the Sine Rule: 11Wassim Al Meniem

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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 12Wassim Al Meniem

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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 13Wassim Al Meniem

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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 37.6 66.6 45.5 31.0 51.1 57.7 92.1 52.3 º 22.9 º 14Wassim Al Meniem

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Remember: Draw a diagramارسم الشكل Label the sidesسمّي الأضلاع Set out your working exactly as you have been shown اجعل عملك منسقا كالذي رأيته بالعرض التقديمي Check your answers regularly and ask for help if you need it تحقق من إجاباتك بشكل منتظم واسأل المدرس للمساعدة 15Wassim Al Meniem

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