Question 747488: I'm stumped on this problem solving a system of equations with unknowns:
A bridge across a river is built in the shape of a circular arc. The middle of the bridge is ten meters above the water, and twenty-seven meters from shore, the bridge is nine meters above the water. How wide is the river?
I've constructed the drawing with the center of the bridge passing thru the y-axis. Here's the equations for the 4 points on the circle:
(1) (-h)^2 + (10-k)^2 = r^2
(2) (w/2 - h)^2 + (-k)^2 = r^2
(3) (-w/2 - h)^2 + (-k)^2 = r^2
(4) (w/2-27-h)^2 + (9-k)^2 = r^2
Equation (1) h^2 + (10-k)^2 = r^2, since h=0, reduces to (10-k)^2 = r^2, or 10-k = r
Equations (2) and (3) reduce to (w/2)^2 + k^2 = r^2, again since h=0
Equation (4) reduces to (w/2-27)^2 + (9-k)^2 = r^2, again since h=0
I can't seem to solve this system of equations, I've multiplied these out several times and tried to group or eliminate common factors, but I'm missing something. Can someone show me the steps?
Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The problem states
A bridge across a river is built in the shape of a circular arc. The middle of the bridge is ten meters above the water, and twenty-seven meters from shore, the bridge is nine meters above the water. How wide is the river?
The following web reference shows us the type of bridge we are dealing with:
http://en.wikipedia.org/wiki/File:MainStPano.jpg
looks like the river is 2*27 or 54 meters wide
Answer by Alan3354(69443)  (Show Source):
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