9 4 the law of cosines
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This document discusses using the law of cosines to solve for unknown sides or angles of a triangle when given certain information about the triangle. It derives the law of cosines formula, provides examples of using it to find a side length when given two sides and the angle between them and to find all angle measures when given all three side lengths, and includes a practice problem to find the length of a median to the longest side of a triangle when given the three side lengths.
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9 4 the law of cosines
- 1. Objectives: 1. Use the law of cosines to find unknown parts of a triangle.
- 2. When to use Law of Cosines ï‚—We know both SAS and SSS determine unique triangles. ï‚—Law of Cosines can be used to solve a triangle for either case.
- 3. Deriving Law of Cosines ï‚—By the distance formula:
- 4. Example 1: Two sides of a triangle have lengths 3 cm and 7 cm and the angle between them is 130°. Find the length of the third side.
- 5. Alternate Form ï‚—Solving the law of cosines for cos C gives: which is used to find angles when all 3 side lengths are given.
- 6. Example 2: ï‚—The lengths of the sides of a triangle are 5, 10, and 12. Solve the triangle.
- 8. You Try! ï‚—A triangle has side lengths 6, 12 and 15. Find the length of the median to the longest side.
- 9. What to Use: