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53. A 60-foot drawbridge is 24 feet above water level when closed. When opened the bridge makes an angle of 33 degrees with the horizontal.
a. How high is the tip P of the open bridge above the water?
b. When the bridge is open, what is distance from P to Q?
53. A 60-foot drawbridge is 24 feet above water level when closed. When opened the bridge makes an angle of 33 degrees with the horizontal.
a. How high is the tip P of the open bridge above the water?
b. When the bridge is open, what is distance from P to Q?

  • trig -

    Does the drawbridge open at the middle, with both ends tilting upward? Where are P and Q?

  • trig -

    Let the open bridge form a trapezoid ABPQ, with bases AB and PQ

    AB = 60
    AP = QB = 30

    height is h such that h/30 = sin 33° = .5446
    h = 16.3 ft

    PQ = 60 - 2*30*cos33° = 9.7 ft

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