Question

A person riding a circular Ferris wheel sits 65 feet from the center. If they travel a distance of 92 feet during an initial rotation, then what radian angle did they rotate through? Round your answer to the nearest hundredth.

Answer 1

we know that
the radius is 65 ft
circumference of a circle=2*pi*r
for r=65 ft
circumference of a circle=2*pi*65-----> 130*pi ft

if 2*pi (full circle) has a length of----------------> 130*pi ft
x------------------------------------------> 92 ft
x=92*2*pi/(130*pi)----------> x=1.4154 radians-------> x=1.42 radians

the answer is
1.42 radians