Question 1136270: Suppose a railroad rail is 2 kilometers and it expands on a hot day by 15 centimeters in length.
Approximately how many meters would the center of the rail rise above the ground?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Given that the railroad rail is  before expansion.
When the railroad expands, it makes an isosceles triangle at the center of the rail.
The base of the triangle is while each leg of the triangle is given by  .
[recall that  , thus  gives  ]
Taking one half of the isosceles triangle, we have a right triangle with one of the leg as  and the  .
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  , then
Thus, the center of the rail will rise  above the ground.
But, there are  in  , therefore, the center of the rail will rise  above the ground.
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