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5 April, 14:13

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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  1. 5 April, 14:33
    0
    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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