Question 179555
It would help you if you were to draw a diagram of the situation in which the right triangle's height represents the height of the roller coaster (105 ft.) and the triangle's base represents the roller coaster's distance from the start of the hill to the top of the hill (200ft.). 
To answer the question "How far do you actually travel on the roller coaster's track?", you need to find the length of the hypotenuse of the right triangle.  This can be done using the Pythagorean theorem: {{{c^2 = a^2+b^2}}} where c is the hypotenuse and a and b are the lengths of the other two legs.  So...
{{{c^2 = a^2+b^2}}} Substitute a = 200ft. and b = 105ft.
{{{c^2 = (200)^2+(105)^2}}}
{{{c^2 = 40000+11025}}}
{{{c^2 = 51025}}} Take the square root of both sides of the equation.
{{{c = sqrt(51025)}}} Using your calculator, you get...
{{{highlight(c = 225.887)}}} Rounding to the nearest foot, you get...
c = 226 feet as the distance actually traveled on the roller coaster's track.