Law of Cosines Homework - LCPS



Law of Cosines Worksheet

Law of Cosines:______________________, ________________________, _____________________

Questions:

|1. When should you use the Law of Cosines to solve a triangle? |2. To solve a triangle in which two sides and the included angle are given, |

| |your tutor suggests that you… |

| |Use Law of Cosines to find the largest angle. |

| |Use Law of Sines to find another angle. |

| |Find the third angle by using the formula 180° – A° – B° = C°. |

| |Why is this easier than using the Law of Cosines to find all of the angles of |

| |the triangle? |

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|3. Compare and contrast when the given information to solve a triangle indicates using the Law of Sines versus using the Law of Cosines. |

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Problems: Solve the following.

|1. Given a = 120, c = 180, β = 56°, find the length of the third side of the |2. Given a = 108, b = 132, c = 160, what is the value of the largest angle in |

|triangle. |the triangle? |

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Solve the triangle.

|3. a = 4, b = 3, c = 6 |

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Solve the following problems.

|4. A surveyor walks 380 meters from point A to point B. Then the surveyor |5. A radio tower 500 feet high is located on the side of a hill that makes a |

|turns 80° to the left and walks 240 meters to point C, as in the figure below. |5° angle with the horizontal, as in the figure below. How long should each of |

|What is the approximate length of the marsh? |the guy wires be if they are to connect with the top of the tower and be |

| |secured 100 feet directly above and directly below the base of the tower? |

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|B | |

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|C | |

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|A | |

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|6. In an attempt to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course that was 10° in error, as in the figure |

|below. If the aircraft maintains an average speed of 220 miles per hour, and if the error is discovered 15 minutes after the beginning of the flight, through |

|what angle should the pilot turn to head toward Louisville? |

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