Answer:
17.8 meters
Step-by-step explanation:
Given:
before expansion railroad rail= 4 km
expansion= 16 cm
railroad makes an isosceles triangle at the center of the rail when it expands
The base of the triangle=4 km
As 1km=100,000 cm
thus 16 cm= 16/100,000 km
each side of this triangle= (4 + 16/100,000) / 2 = 4.0001 / 2 = 2.00008 km
One half of the isosceles triangle makes a right triangle with one of the side =4 / 2 = 2 km
and the hypotenuse = 2.00008 km
Using Pythagoras theorem to find the third side of this right angles triangle:
c^2=a^2+b^2
2.00008^2= 2^2 + b^2
2.00008^2 - 2^2=b^2
b=0.0178 km
b= 17.8 m
hence, approximately 17.8 meters would the center of the rail rise above the ground!
