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Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing Upper S 14 degrees Upper W at 440 miles per hour. The other plane travels on a bearing Upper N 75 degrees Upper W at 420 miles per hour. How far are the planes from each other 3 hours after​ takeoff?

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matthewadeyinka10

Answer:

 Let's imagine this is the diagram for the question,

                 •    

3*440=       /  |

               /     |

1320mi  ↑       |

           ↑         ↓

          /           ↓

        /             |

      • ) 89⁰     |

       \              |   "x" miles

         \            ↑

           \          ↑

            ↓         |

              ↓       |      

3*420=      \     |

1260 mi      \   |

                        •

From the Cosine Rule:  x² = y² + z² - 2 y z cos X⁰

x² = 1320² + 1260² - 2 * 1320 * 1260 * cos 89⁰ =  

1742400 + 1587600 - 3326400 * cos 89⁰ = 3271946315  

x ≈ 1809 mi

Hence, the planes are 1809 miles from each other 3 hours after​ takeoff?

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