Question 66857
The tiger trotted through an arc of pi/6 radians along a circular arc of radius 1000 feet. How far did the tiger trot?


Diameter of the circle is 2000ft
C=pi(D)=2000pi feet

A circle contains 2pi radians.  So we can set up a ratio

2pi is to 2000pi as pi/6 is to x

2pi/2000pi=(pi/6)/x   the left side reduces:

1/1000=(pi/6)/x  multiply both sides by x
x/1000=pi/6  multiply through by 6000
6x=1000pi
x=166.6667 (3.14)=523.3333ft

Another way to look at it:

pi/6 radians =30 degrees which projects an arc equal to 1/12 the circumference of the circle:

1/12(2000pi)=166.667pi=523.3333ft


Hope this helps------ptaylor