A bridge

A bridge over a river has the shape of the arc with bases of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. How wide is the river?

Correct result:

a =  80 ft

Solution:

r=10+x r2=x2+(27+y)2 r2=(9+x)2+y2  (10+x)2=x2+(27+y)2 (10+x)2=(9+x)2+y2  20 x=y2+54 y+629 2 x+19=y2  20(y219)/2=y2+54y+629  20 (y219)/2=y2+54 y+629 9y254y819=0  a=9;b=54;c=819 D=b24ac=54249(819)=32400 D>0  y1,2=b±D2a=54±3240018 y1,2=54±18018 y1,2=3±10 y1=13 y2=7   Factored form of the equation:  9(y13)(y+7)=0  x>0;y>0;r>0  y=y1=13=13 ft x=(y219)/2=(13219)/2=75 ft r=10+x=10+75=85 ft  a=2 27+2 y=2 27+2 13=80 ft

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Showing 2 comments:
#
Dr Math
THE BRIDGE OVER THE RIVER

#
Dr Math
r = radius of circle of arc

x = distance between center of circle and water level (center of the circle is under ground)

y = distance in horiznotal of point on circle which is 9 ft above the water

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