Pythagorean Theorem Word Problem

Question

A 1 mile piece of rail is cut in half. Each end has one side/end bolted to the ground. The other two ends are touching each other. In the heat of the day, each half mile of rail expands 1/2 an inch. This causes the 2 half pieces of rail to expand and push up in the spot where they meet. How far above the ground level does each half mile of rail rise? Make a drawing and show your work. Assume the rail and ground are all level and straight. Hint: remember the pythagorean theorem.

Answer 1

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The rail form 2 right triangles. Each has one side 1/2 mile long, and a hypotenuse 1/2 mile plus 1/2 Inch long. So you have two trialing each of which has length of 31,680 inches and hypotenuse of 31,680.5 inches and you have to find the height of the short leg. 

 

Square the hypotenuse and the long leg.

Deduct the square of the long leg from the square of the hypotenuse to find the square of the short leg.

Find the square root of the square of the short leg to find the length of the short leg.

 

The short leg should be 177.98 inches high