A circle of radius 10m has a circumference C = 2πR = 62.83 m. A 30° angle would intercept an arc that is 30/360 or 1/12 of this, namely 5.24 m. What does this result (along with the result in the previous problem) suggest about the validity of the formula derived in Box 1-1? [Note to instructors: This question and the previous one are intended to reinforce concept that the small angle formula computes subtended arc length, which is slightly greater than D in Box 1-1 for large angles, but a reasonably good approximation for small angles.]
A)The formula is valid even for angles as large as 30°.
B)The formula actually calculates the length subtended by a given angle at a given distance. Thus the formula computes a length that is longer than length D in Box 1-1.
C)The formula actually calculates the length subtended by a given angle at a given distance. Thus the formula computes a length that is shorter than length D in Box 1-1.
D)The formula is valid for angles larger than 30° but not for angles smaller than 30°.

Question

Quizplus · Accepted Answer

The result suggests that the formula actually calculates the length subtended by a given angle at a given distance, which is slightly greater than length D in Box 1-1 for larger angles, but still a reasonably good approximation for small angles. The fact that a 30° angle intercepts an arc length of 5.24 m, which is greater than the chord length of 10 sin(30°) = 5 m, supports this explanation. Therefore, option B is the correct choice.

A Circle of Radius 10m Has a Circumference C =