Find radius knowing chord length and height?

Question

I'm building a long foot bridge and am trying to figure radius. My bridge will span 110 ft. and rise seven ft.

Answer 1

I assume you are talking about the bridge being a circular arc since you mentioned a radius. If you draw a diagram, the bridge will be at maximum height in the middle, or 55 feet from each end. Then we have a right triangle.

Let r = radius of circle.

The legs are 55 and (r - 7).
The hypotensuse is r.

So we have

r² = (r - 7)² + 55²
r² = r² - 14r + 49 + 3025
14r = 3074
r = 3074 / 14 = 1537 / 7 = 219 4/7 feet

You might want to ask yourself if you really want to make the bridge a circular arc.

Answer 2

you should use Pythagoras' theorem; notwithstanding the theory of intersecting chords will be faster: Co0nsider the diameter perpendicular for your chord. It bisects the chord;; and is itself divided into 2 parts by the chord : a million, and (say) x. So 4*4 = a million*x. So the diameter is 17; and the radius 8.5 .

Answer 3

its a parabola. not a circle. any bridge is a parabola, and not a cirlce, though it looks like one.
the bridge you are talking about is an open downward parabola.