document.write( "Question 982633: The arch of a bridge is an arc of a circle. The distance between the ends of the arc is 56 cm and the clearance of the arch above the water is 9.8 m. Find the radius of the arc. \n" ); document.write( "

Algebra.Com's Answer #603537 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The arch of a bridge is an arc of a circle.
\n" ); document.write( " The distance between the ends of the arc is 56 METERS and the clearance of the arch above the water is 9.8 m.
\n" ); document.write( " Find the radius of the arc.
\n" ); document.write( ":
\n" ); document.write( "draw this out. The chord of the circle will be 56 m long.
\n" ); document.write( "let x = dist from center and middle of the chord, (the water)
\n" ); document.write( "then the radius will be (x+9.8)
\n" ); document.write( ":
\n" ); document.write( "Note; two right triangles formed by half the chord (28m), x,
\n" ); document.write( " and the radius (hypotenuse)
\n" ); document.write( ":
\n" ); document.write( "Using pythag; a^2 + b^2 = c^2, we can write this problem like this
\n" ); document.write( " $\"sqrt%28x%5E2+%2B+28%5E2%29\"$ = r
\n" ); document.write( "replace r with (x+9.8)
\n" ); document.write( " $\"sqrt%28x%5E2+%2B+28%5E2%29\"$ = x + 9.8
\n" ); document.write( "Square both sides
\n" ); document.write( "x^2 + 28^2 = (x+9.8)^2
\n" ); document.write( "FOIl the right side
\n" ); document.write( "x^2 + 784 = x^2 + 19.6x + 96
\n" ); document.write( "Subtract x^2 and 96 from both sides
\n" ); document.write( "784 - 96 = 19.6x
\n" ); document.write( "19.6x = 688
\n" ); document.write( "x = 688/19.6
\n" ); document.write( "x = 35.1
\n" ); document.write( "Find the radius
\n" ); document.write( "r = 35.1 + 9.8
\n" ); document.write( "r = 44.9 meters is the radius
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