1. 1 Equations 7.3 The Law of Cosines 7.4 The Area of a Triangle Chapter 7

2. 2 In any triangle ABC, with sides a, b, and c. In any triangle ABC, with sides a, b, and c. Thus, in any triangle, the square of a side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle between them. Thus, in any triangle, the square of a side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle between them. 7.3 Law of Cosines

3. 3 Example 1 Solve  ABC if a = 4, c = 6, and B = 105.2 . Solve  ABC if a = 4, c = 6, and B = 105.2 . A C B b 6 105.2  4

4. 4 Example 2 Solve  ABC if a = 15, b = 11, and c = 8. Solve  ABC if a = 15, b = 11, and c = 8. Solve for A first Solve for A first 15 11 8 A B C

5. 5 The area A of a triangle is where b is the base and h is the altitude drawn to that base. 7.4 Area of a Triangle

6. 6 h b a

7. 7 In any triangle ABC, the area A is given by the following formulas: In any triangle ABC, the area A is given by the following formulas:

8. 8 Example: SAS Find the area of the triangle, ABC with A = 72 , b = 16 and c = 10. Find the area of the triangle, ABC with A = 72 , b = 16 and c = 10. Solution: Solution: 10 A B C 16 72 

9. 9 The area A of a triangle equals one-half the product of two of its sides times the sine of its included angle.

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11. 11 Heron’s Formula The area A of a triangle with sides a, b, and c is

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