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How do you find the radius of a circle given the length of an arc?

Answer 1

Theodore Abad

The circle with radius #r# has a circumference #2*pi*r# which corresponds to an angle of #360^o#.

If you are given an arc of a certain angle lets say #p^o# degrees which is #l# in length then

#p^o/360^o=l/(2*pi*r)=>r=(360^o*l)/(2*pi*p^o)#

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Answer 2

Sadie Allen

#r = (180 xxl)/( pi theta)#

You always need another piece of information, just the arc length is not enough - the circle could be big or small and the arc length does not indicate this.

It will help to be given the sector angle.

If you have the sector angle #theta#, and the arc length, #l# then you can find the radius

#r = (180 xxl)/(pi theta)#

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Answer 3

Mason Adams

To find the radius of a circle given the length of an arc, you can use the formula:

[ r = \frac{L}{\theta} ]

Where:

( r ) is the radius of the circle.
( L ) is the length of the arc.
( \theta ) is the angle subtended by the arc (in radians).

Alternatively, you can use the formula:

[ r = \frac{L}{2 \cdot \sin\left(\frac{\theta}{2}\right)} ]

Both formulas give you the radius of the circle based on the length of the arc and the angle subtended by the arc.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.