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The Sine Rule قاعدة الجيب. *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. G. B. 2. 1. 53 º. 41 º. x. 62 º. A. x.

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## The Sine Rule قاعدة الجيب

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**The Sine Ruleقاعدة الجيب**Wassim Al Meniem***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. Wassim Al Meniem**G**B 2. 1. 53º 41º x 62º A x 5 cm º 76º C H 26 mm I 2. 1. 82º 47º 5 cm 8.2 cm xº xº 6 cm Wassim Al Meniem**a**sinA b sinB c sinC = = The Sine Rule can be used for any triangle: تستخدم مع أي مثلث C b The sides are labelled to match their opposite angles a A B c The Sine Rule: Wassim Al Meniem**a**sinA b sinB c sinC = = The Sine Rule can be used for any triangle: C The sides are labelled to match their opposite angles b a A B c The Sine Rule: Wassim Al Meniem**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 ارسم مستقيم من الضلع للزاوية المقابلة له ليساعدك على التعويض بالقاعدة. x = ×sin76º x = 7.6 cm Wassim Al Meniem**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 Wassim Al Meniem**G**B 3. 1. 2. F 53º 13 cm 41º x x 62º A x 130º 28º D E 5 cm 63º 76º C H 26 mm I 4. 5.2 cm 5. x 61º R 6. P 37º 66º 57º 10 m 35º x 77º 62º Q 12 cm 6 km 85º 7. x 65º 86º x Wassim Al Meniem**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 Wassim Al Meniem 6.9**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 regularlyand ask for help if you need it تحقق من اجاباتك بشكل منتظم واسأل المدرس للمساعدة Wassim Al Meniem**sinA**a sinB b sinC c = = Finding an Angleإيجاد 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 Alternative form of the Sine Rule: Wassim Al Meniem**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 Wassim Al Meniem**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 Wassim Al Meniem**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 Wassim Al Meniem**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 regularlyand ask for help if you need it تحقق من إجاباتك بشكل منتظم واسأل المدرس للمساعدة Wassim Al Meniem

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