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Published byQuentin Derick Sharp Modified over 10 years ago
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The sine rule When the triangles are not right-angled, we use the sine or cosine rule. Labelling triangle Angles are represented by upper cases and sides by lower cases. Length a is labelled to the side which is opposite to the angle A., and so on.
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The sine rule formulae We use this formula to find sides. We use this formula to find angles.
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Examples: finding unknown sides 45 60 C 8 cm b c In triangle ABC, find, in cm to 3 s.f., the length b. b 9.80 cm 40 68 C 9 cm b c In triangle ABC, find, in cm to 3 s.f., the length c. Angle C = 180 – 40 – 68 = 72º c 13.3 cm
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Examples: finding unknown angles Find angle B. sinB 0.3054…. 110 6.5cm 20cm B B =sin -1 (0.3054…) =17.8º
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Examples: finding unknown angles Find, in degrees to 1 d.p., the size of the angle B and A in the triangle, where C = 40° and b = 7cm and c = 5cm. 40 ° 7 cm 5 cm A C B B The sketch shows that there may be two possible triangles which fit the information. B = sin -1 (0.8999..) = 64.1° or 180- 64.1 =115.9° A = 180 – 64.1 – 40 = 75.9° or 180 – 115.9 – 40 = 24.1°
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The area of a triangle Area = ½ absin C where C is the included angle between sides a and b. a b C 55 ° 6 cm 7 cm Area = ½ x 6 x 7 x sin55 = 17.2 cm 2 40 ° 9 cm 10 cm Let a = 9, b = 10, A = 40 B = 45.6º C = 180 – 40 – 45.6 = 94.4Area = ½ x 9 x 10 x sin94.4 = 44.9 cm 2
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Trig worksheet A Question 1
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Trig worksheet A Question 2
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