Suppose a railroad rail is 6 kilometers and it expands on a hot day by 10 centimeters in length. approximately how many meters would the center of the rail rise above the ground?

Given that the railroad rail is 6 kilometers before expansion.

When the railroad expands, it makes an isosceles triangle at the center of the rail.

The base of the triangle is 6 kilometers while each leg of the triangle is given by (6 + 10/100,000) / 2 = 6.0001 / 2 = 3.00005 kilometers.
[recall that 100,000 centimeters gives 1 kilometers, thus 10 centimetres gives 10/100,000 kilometers]

Taking one half of the isoceles triangle, we have a right triangle with one of the leg as 6 / 2 = 3 kilometers and the hypothenus = 3.00005 kilometers.

Thus, using the Pythagoras theorem, we find the other leg (height) of the right triangle as follows.

Let the other leg of the right triangle be h, then


Thus, the center of the rail will rise 0.01732058 kilometers above the ground.

But, there are 1,000 meters in 1 kilometers, therefore, the center of the rail will rise 0.01732058 x 1,000 = 17.32 meters above the ground.