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john's paint crew knows from experience that its 18 ft ladder is particularly stable when the distance from the ground to the top of the ladder is 5 ft more than the distance from the building to the base of the ladder. in this position, how far up the building does the ladder reach?

  • functions - ,

    Functions?

    This is a geometry problem.

    The ladder up against the wall forms a right triangle.

    x = base
    x + 5 = opposite side
    18 = hypotenuse

    Using the Pythagorean theorem,
    x^2 + (5 + x)^2 = 18^2

    Solve for x

    5 + x = how far up the blding the ladder reaches.

  • functions - ,

    let the base be x ft
    then the height is x+5 ft

    solve x^2 + (x+5)^2 = 18^2

  • functions - ,

    14.98?

  • functions - ,

    x = 9.989983874

    Use that answer to check your work.

    (9.979983874)^2 + (9.979983874 + 5)^2 = 18^2

    The height is exactly 14.979983874 ft.

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