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

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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.

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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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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.

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.

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.

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- A cone has a height of #6 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?
- Two corners of an isosceles triangle are at #(3 ,9 )# and #(6 ,7 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?
- What is the area of these two figures?

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