Suppose a railroad rail is 4 kilometers and it expands on a hot day by 16 centimeters in length. approximately how many meters would the center of the rail rise above the ground?

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!

b

step-by-step explanation: