SOLUTION: 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?

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?
Answer by rothauserc(4718) (Show Source): 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
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therefore, for the semicircle we have y = square root(r^2 -x^2), where the square root is positive for the semi circular tunnel
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let the center for the semicircle tunnel be (0,0), then
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the outside edges of the two lanes are -14 and 14
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Note that y is the height of the tunnel
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y = square root(256-x^2)
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y = square root(256-196) = 7.746
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the tunnel is 7.746 feet high at each edge
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