2. { Law of Sines and Cosines Trigonometry applied to triangles without right angles. 1

3.  You have learned to apply trigonometry to right angled triangles. 2 A hyp adj opp

4.  Now we extend our trigonometry so that we can deal with triangles which are not right angled. 3

5.  First we introduce the following notation.  We use capital letters for the angles, and lower case letters for the sides. 4 Q q p r R P A a b c C B In  ABC The side opposite angle A is called a. The side opposite angle B is called b. In  PQR The side opposite angle P is called p. And so on

6.  There are two new rules. 5

7. 1. The Law of Sines 6 A a b C c B.

8.  Find the length of BC. 7 Substitute A = 35 o, B = 95 o, b = 6.2: Multiply by sin35 o : A a 6.2 cm c C B 35 o 95 o

9.  one for finding a side,  one for finding an angle. There are two main ways of writing the Law of Cosines 8 Law of Cosines

10. The Law of Cosines (to find the length of a side) 9 A a b c C B

11. The cosine rule for finding an angle 10

12.  To use the sine rule you need to know an angle and the side opposite it. You can use it to find a side (opposite a second known angle) or an angle (opposite a second known side).  To use the cosine rule you need to know either two sides and the included angle or all three sides. How do I know whether to use the sine rule or the cosine rule?