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March 27, 2017

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A bridge is the shape of an arc of a circle. The bridge is 8 feet tall and 36 feet wide. What is the radius of the circle that contains the bridge? Round your answer to the nearest tenth.

  • Geometry (immediate help and explanation) - ,

    Assuming that the 36 feet wide line base is NOT a diameter, make a sketch
    let the radius be x
    then I see a right-angled triangle where
    (x-8)^2 + 18^2 = x^2
    x^2 - 16x + 64 + 324 = x^2
    -16x = -388
    x = 24.25

  • Geometry (immediate help and explanation) - ,

    Thanks! But one question..um, where did you get the triangle?

  • Geometry (immediate help and explanation) - ,

    draw a whole circle

    draw a chord AB, your base , = 36
    From the centre O draw a line OA , a radius
    let the radius be x
    so OA = x, the hypotenuse

    from the centre draw a perpendicular to AB to hit AB at C
    from C to the circle is 8 , so OC = x-8
    OCA is a right - angled triangle.
    so ...
    see above

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