Aperson 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.

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

I started by labeling the right angle (Angle C) 90º. Next, I wrote down everything in one equation.

2x + 90 + 3x - 20 = 180º (180 degrees in a triangle)

Next, I add 20 on both sides.

2x + 90 + 3x = 200º

I combine like terms (2x and 3x)

5x + 90 = 200º

I subtract 90 from both sides.

5x = 110º

Divide 110 by 5 to get x.

x = 22

For problem two, I label all the angles I know.

49º + 80º + r = 180º

I add 80 and 49.

129º + r = 180º

I subtract 180 and 129 and get 51º, which is your angle for R.

For angle X, you know that angle R plus angle X equals half of a circle, which is 180º

We know from before that 129º is 180º without R, so X is 129º

I hope this helps! Let me know if I'm wrong!