The ropes on either side of a swing are 1.9 m long. if a child swings through a arc length of 0.9 determine the angle (in radians) through which the child swings

theta = 9/19 radians or  approximately .4737 radians

Step-by-step explanation:

The formula for arc length is

S = r theta  

where theta is in radians.  Lets put in what we know.  The radius would be 1.9 since the ropes would be the radius.

.9 = 1.9 theta

Divide by 1.9 on each side.

.9/1.9 = theta

theta = 9/19 radians

or in decimal form it is approximately  .4737 radians