Expert: Bobby Soltani - 2/13/2005

Question
Can you assist me with resolving the following problems: I need to see
how it's done. I know the formula to use, but know how to apply it to these word problems.  

1. Find the length of an arc in inches for a circle whose radius is 15 inches
and subtends a central angle of 45 degrees.



2. The pednulm of a clock, 27 inches long, swings through an arc of 21 degrees
for its resting position. find the distance a point 1/3 the distance from the
tip of the pendulum travel in one swing.  

Answer
Hi Adrienne,

The equation we want to use is s = r*t, where s is the arc length, r is the radius of the circle, and t is the angle in radians.  To get radians from degrees, we use the equation
radians = degrees*pi/180

1.  we want to find s when r = 15 and t = 45*pi/180 = 0.785 radians.

Therefore,
s = 15*0.785 = 11.775 inches

2.  A distance 1/3 from the tip would be 2/3 the length of the pendulum.  So r = 27*(2/3) = 18, and the degrees is still 21.  So, r = 18 and t = 21*pi/180 = 0.367 radians.  Therefore,

s = 18*0.367 = 6.597 inches.

Let me know if you have any questions.

Bobby