Cosh Bridge Length

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Finding the Length of a Hyperbolic Cosine Shaped Bridge

You are a structural engineer in charge of the design of the bridge shown below. As pictured, the shape of the bridge will be the same as the shape of the hanging rope that holds it together, or the catenary $y=a\cdot \cosh(\frac{x}{a})$ where $a$ represents the number of feet the lowest point of the bridge will be above the river. You will be given $a$ and how far the bridge will extend from the center of the river, and it will be your job to determine the total length of the bridge, so that the appropriate amount of material is ordered. Round your answer to two decimal places.

$bridge.JPG$

Click Begin to see the height of the bridge and the horizontal distance from the beginning and end to the center.

The length of the bridge will be feet.

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