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Law of Sines and Cosines

Law of Sines and Cosines. Trigonometry applied to triangles without right angles. hyp. opp. A. adj. You have learned to apply trigonometry to right angled triangles. Now we extend our trigonometry so that we can deal with triangles which are not right angled. B. P. q. c. a. r. R.

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Law of Sines and Cosines

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

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

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

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

  5. There are two new rules.

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

  7. B 95o c a 35o C A 6.2 cm • Find the length of BC. • Substitute A = 35o, B = 95o, b = 6.2: • Multiply by sin35o:

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

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

  10. The cosine rule for finding an angle

  11. 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?

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