Answer:
Center of the rail rise above the ground in 17 m.
Solution:
The railroad rail is 3 km = 3000 meter
It expands 20 cm = 0.2 meter on hot day in length
So it will form a triangle with base 3000 m and the equal sides will be [tex]\frac{3000+0.2}{2} meter = 1500.1 meter[/tex]
Let us assume that the center of the rail will raise x meter.
So using Pythagoras theorem,
[tex]x^{2}+1500^{2}=1500.1^{2}[/tex]
[tex]x^{2}=1500.1^{2}-1500^{2}[/tex]
[tex]x^{2}=(1500.1+1500)(1500.1-1500)[/tex]
[tex]x=3000.1\times0.1[/tex]
[tex]x^{2}=300.01[/tex]
Taking square roots on both sides we get,
[tex]x=17(\text {approx})[/tex]
So, the rail raise 17 meter from the ground .
