Suppose an arc were intercepted by a central angle measuring 15°. The diameter of the circle is 9 cm. Can both of these values be substituted into the arc length formula? Explain

Question

Lance Campbell

Mathematics

23 October, 08:36

Suppose an arc were intercepted by a central angle measuring 15°. The diameter of the circle is 9 cm. Can both of these values be substituted into the arc length formula? Explain

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Answers (1)

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Parker · Answer 1

NO, because this angle is being expressed in degrees and not in radians (the formula needs the angle to be in radians)

Step-by-step explanation:

The arc formula is the following:

arc length = angle * radius

with the angle in radians.

So the answer is NO, because this value of angle (15 degrees) is being expressed in degrees and not in radians. To use the formula, we would first need to convert from degrees to radians:

2pi radians - > 360 degrees

x radians - > 15 degrees

x = 15 * 2pi / 360 = 0.2618 rad

Now we can use this angle to find the arc:

arc = 0.2618 * 9 = 2.3562 cm