Given a circle with a radius of 6 and a central angle measure of 60 degrees. Therefore, the arc length is 2pi units.
How to find the relation between the angle subtended by the arc, the radius and the arc length?
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows the angle measured in radians.
If the radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
Given a circle with a radius of 6 and a central angle measure of 60 degrees,
360 degrees = 1 circle
The fraction 60/360 = 1/6 of the circumference
[tex]c=2\pi r\\c=2\pi \times 6\\c=12\pi[/tex]
so
Therefore, the arc length is 2pi units.
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