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Sine Rule for Angles

P. Q. R. 18 20. =. sin42 ° sinQ°. p q r. = =. sinP sinQ sinR. Sine Rule for Angles. Ex1. 42 °. 20cm. 18 X sinQ ° = 20 X sin42°. sinQ ° = 20 X sin42°  18. 18cm. sinQ ° = 0.743…. (min 3 dps). Find angles Q and R. Q ° = sin -1 0.743. = 48 °. . .

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Sine Rule for Angles

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  1. P Q R 18 20 = sin42° sinQ° p q r = = sinP sinQ sinR Sine Rule for Angles Ex1 42° 20cm 18 X sinQ° = 20 X sin42° sinQ° = 20 X sin42°  18 18cm sinQ° = 0.743…. (min 3 dps) Find angles Q and R. Q° = sin-10.743 = 48°   R° = 180° – 42° - 48°  ? ? = 90°

  2. F G H 30 17 = sin72° sinH° f g h = = sinF sinG sinH Ex2 72° 17cm 30 X sinH° = 17 X sin72° sinH° = 17 X sin72°  30 30cm sinH° = 0.539.…. (min 3 dps) Find angles G and H. H° = sin-10.539 = 32.6°   R° = 180° – 72° - 32.6°  ? ? = 75.4°

  3. Ex3 3.2 1.7 X = sinc° sin32° 3.2m 1.7m x y z c° = = 32° Y Z sinX sinY sinZ In a lop-sided roofthe longer side is 3.2m and slopes at an angle of 32° to the horizontal. The shorter side is 1.7m and makes an angle of c° with the horizontal. Find c°. 3.2m 1.7m c° 32° 1.7 x sinc° = 3.2 x sin32° sinc° = 3.2 x sin32°  1.7  sinc° = 0.997  c° = sin-10.997  ? = 86°

  4. Obtuse Angles A B A+B sinA° sinB° 20 160 180 0.342 0.342 35 145 180 0.574 0.574 70 110 180 0.940 0.940 43 137 180 0.682 0.682 CONCLUSION If A + B = 180 then sinA° = sinB° Ex4 sinx° = 0.643 so x = sin-10.643 = 40° or 140°

  5. B 4cm A 30° C 7cm a b c = = sinA sinB sinC Ex5 In ABC a = 4, b = 7 & angle A = 30°. Find two possible sizes for angle B. 

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