Question

A footbridge is in the shape of an arc of a circle. The bridge is 4.5 ft tall and 25 ft wide. What is the radius of the circle that contains the bridge? Round to the nearest tenth.

Answer 1

Assuming that the 36 feet wide line base is NOT a diameter, make a sketch

let the radius be x

then I see a right-angled triangle where

Explanation:

(x-8)^2 + 18^2 = x^2

x^2 - 16x + 64 + 324 = x^2

-16x = -388

x = 24.25

draw a chord AB, your base , = 36

From the centre O draw a line OA , a radius

let the radius be x

so OA = x, the hypotenuse

from the centre draw a perpendicular to AB to hit AB at C

from C to the circle is 8 , so OC = x-8

OCA is a right - angled triangle.