Law of Sines Homework



Law of Sines & Cosines Homework Worksheet

Law of Sines: ______________________________________________________________________

Law of Cosines:______________________, ________________________, _____________________

Questions: Answer the questions and justify your answers.

|1. To use the Law of Sines, you must know the |2. Is it possible to solve a triangle if you |3. Why is it not generally possible to use the |

|measures of at least… |only know the measures of the three angles in the|Law of Sines to solve a triangle for which one |

| |triangle? |only knows the measures of all of the sides in a |

| | |triangle? |

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|4. When should you use the Law of Cosines to |5. To solve a triangle in which two sides and the included angle are given, your tutor suggests |

|solve a triangle? |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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|6. 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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Solve the triangles.

|7. β = = 82°, b = 6, c = 3 |8. α = 42°, a = 10, c = 18 |

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|9. γ = 32°, a = 14, c = 9 |

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|10. a = 4, b = 3, c = 6 |

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|11. To find the distance across a canyon, a surveying team locates points |12. A surveyor walks 380 meters from point A to point B. Then the |

|A and B on one side of the canyon and point C on the other side of the |surveyor turns 80° to the left and walks 240 meters to point C, as in the |

|canyon. The distance between points A and B is 85 yards. The measure of |figure below. What is the approximate length of the marsh? |

|[pic]CAB = 68°, and the measure of [pic]ABC = 75°. What is the distance | |

|across the canyon? | |

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| |B |

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| |C |

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| |A |

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