document.write( "Question 1120520: A street in manila composing of two lanes each 14ft wide runs through a semi circular tunnel with a radius of 16ft. What is the height of the tunnel at the edge of each lane? \n" ); document.write( "

Algebra.Com's Answer #736178 by rothauserc(4718) $\"\"$ $\"About$

You can put this solution on YOUR website!
for a circle, we know x^2 +y^2 = r^2, where r is the radius of the circle
\n" ); document.write( ":
\n" ); document.write( "therefore, for the semicircle we have y = square root(r^2 -x^2), where the square root is positive for the semi circular tunnel
\n" ); document.write( ":
\n" ); document.write( "let the center for the semicircle tunnel be (0,0), then
\n" ); document.write( ":
\n" ); document.write( "the outside edges of the two lanes are -14 and 14
\n" ); document.write( ":
\n" ); document.write( "Note that y is the height of the tunnel
\n" ); document.write( ":
\n" ); document.write( "y = square root(256-x^2)
\n" ); document.write( ":
\n" ); document.write( "y = square root(256-196) = 7.746
\n" ); document.write( ":
\n" ); document.write( "the tunnel is 7.746 feet high at each edge
\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "

\n" );