the arch of a concrete bridge is a semi ellipse having a span of 60 ft and a central height of 20 ft. if the roadway is 25 ft above the base. find at 10 ft intervals the distance from the arch to the roadway. (Im completely lost at what to find. Please help)

Answer 1

what you have is an ellipse with semi-axes of 30 and 20 ft, with the long axis horizontal. So, if the center is placed at (0,0) the equation is

x^2/30^2 + y^2/20^2 = 1

So, the upper arch is

y = 4/9 √(900-x^2)

Now just plug in your various values for x to find the height y.