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

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Question 66857This question is from textbook Advanced mathematics
: The tiger trotted through an arc of pi/6 radians along a circular arc of radius 1000 feet. How far did the tiger trot?
This question is from textbook Advanced mathematics

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
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