Precalculus/trigonometry angles involving lengths?

To approximate the length of a marsh, a surveyor walks 425 meters from point A to point B. Then the surveyor turns 65º and walks 300 meters to point C. Approximate the length AC of the marsh.

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  • 5 months ago

    Use law of the cosine.

    a²+b²-2abCOS(°)=c²

    425²+300²-2*425*300*cos(180-65)=615.14²

    AC length = 615.14m

    Attachment image
  • ?
    Lv 7
    5 months ago

     To approximate the length of a marsh, 

     a surveyor walks 425 meters from point A to point B. 

     Then the surveyor turns 65° and walks 300 meters to point C. 

     The length AC of the marsh is 403.55587 meters.

  • Use the law of cosines

    (AC)^2 = 425^2 + 300^2 - 2 * 425 * 300 * cos(65)

    (AC)^2 = 25^2 * (17^2 + 12^2 - 2 * 17 * 12 * cos(65))

    (AC)^2 = 25^2 * (289 + 144 - 2 * 204 * cos(65))

    (AC)^2 = 25^2 * (433 - 408 * cos(65))

    AC = 25 * sqrt(433 - 408 * cos(65))

    Make sure your calculator is in degree mode

    403.5558737722964227259291064567....

    To 3 sf

    404 meters

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