1. 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.

2. The sine rule formulae We use this formula to find sides. We use this formula to find angles.

3. 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

4. Examples: finding unknown angles Find angle B.  sinB   0.3054…. 110  6.5cm 20cm B B =sin -1 (0.3054…) =17.8º

5. 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°

6. 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

7. Trig worksheet A Question 1

8. Trig worksheet A Question 2