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# Properties & Solution of Triangles

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### Properties & Solution of Triangles

1. 1. PROPERTIES & SOLUTION OF TRIANGLE
2. 2. SINE RULE
3. 3. EXAMPLES
4. 4. COSINE FORMULA b2 c2 a 2 cos A = or 2bc a² = b² + c² - 2bc cos A = b2 + c2 + 2bc cos (B + C) c2 a 2 b2 cos B = 2 ca a2 b 2 c2 cos C = 2a b
5. 5. EXAMPLES
6. 6. PROJECTION FORMULA a = b cosC + c cosB b = c cosA + a cosC c = a cosB + b cosA
7. 7. EXAMPLES
8. 8. NAPIER’S ANALOGY - TANGENT RULE B C b c A tan cot 2 b c 2 C A c a B tan cot 2 c a 2 A B a b C tan cot 2 a b 2
9. 9. EXAMPLES
10. 10. TRIGONOMETRIC FUNCTIONS OF HALF ANGLES
11. 11. AREA OF TRIANGLE (∆)
12. 12. EXAMPLES
13. 13. M-N RULE m cot n cot n cot B m cot C
14. 14. EXAMPLES