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Pre-Calculus

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A road sign at the top of a mountain indicates that for the next 4 miles the grade is 12%. Find the angle of the grade and the change in elevation for a car descending the mountain.

  • Pre-Calculus - ,

    The grade of an incline is its vertical rise in some units per every 100 horizontal run in the same units.
    so
    rise/run = tan slope = .12
    so slope = tan^-1 .12 = 6.8 degrees
    height in miles = .12 run in miles
    ( the question is ambiguous. I am assuming the 4 miles is on the map, horizontal, rather than on the odometer , hypotenuse)
    height change = .12*4 miles = .48 miles down
    or .48*5280 = 2534 feet down

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