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A pendulum 20 cm long swings 3 degrees 30 minutes on each side of it's vertical position. Find the length of the arc formed by the tip of the pendulum.

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1 Answer

The formula for the length of an arc on a circle is:
 
Arc Length = θ*r
 
Where r is the radius of the circle and θ is the angle subtended by the arc, measured in radians.  Note that for a full circle, θ = 2pi radians and the Arc Length = 2(pi)r, the formula for the perimeter of a full circle.
 
In your problem, we know the radius (r) is 20 cm and the angle is 7 degrees (3.5 degrees on either side of vertical).  All you need to do is convert the 7 degrees to radians then use the Arc Length formula above.  The conversion formula is:
 
7 degrees      180 degrees
----------- =   ---------------
x radians        (pi) radians
 
Solve for x, then plug it into the Arc Length equation along with the radius, r = 20 cm, to compute the arc length.