Sine Rule for Angles Ex1 P Q R 18 20 sin42° sinQ° = 18 20 sin42° sinQ° = 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°   p q r sinP sinQ sinR = = R° = 180° – 42° - 48°  ? ? = 90°

Ex2 F G H 30 17 sin72° sinH° = 30 X sinH° = 17 X sin72° 30 17 sin72° sinH° = 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°   f g h sinF sinG sinH = = R° = 180° – 72° - 32.6°  ? ? = 75.4°

Ex3 In a lop-sided roof the 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° 3.2 1.7 sinc° sin32° = X Y Z 3.2m 1.7m 32° c° 1.7 x sinc° = 3.2 x sin32° sinc° = 3.2 x sin32°  1.7  sinc° = 0.997  x y z sinX sinY sinZ = = c° = sin-10.997  ? = 86°

If A + B = 180 then sinA° = sinB° 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°

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