Question 982633
The arch of a bridge is an arc of a circle.
 The distance between the ends of the arc is 56 METERS  and the clearance of the arch above the water is 9.8 m.
 Find the radius of the arc. 
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draw this out. The chord of the circle will be 56 m long.
let x = dist from center and middle of the chord, (the water)
then the radius will be (x+9.8)
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Note; two right triangles formed by half the chord (28m), x,
 and the radius (hypotenuse)
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Using pythag; a^2 + b^2 = c^2, we can write this problem like this
{{{sqrt(x^2 + 28^2)}}} = r
replace r with (x+9.8)
{{{sqrt(x^2 + 28^2)}}} =  x + 9.8
Square both sides
x^2 + 28^2 = (x+9.8)^2
FOIl the right side
x^2 + 784 = x^2 + 19.6x + 96
Subtract x^2 and 96 from both sides
784 - 96 = 19.6x
19.6x = 688
x = 688/19.6
x = 35.1
Find the radius
r = 35.1 + 9.8
r = 44.9 meters is the radius