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Let us recall the formula for the circumference of a circle. That one is 2pi r. r is the radius of the circle and 2pi is the angle in radian measure subtended by the entire circle at the centre. If this is so, then any arc length 'l' will be equal to the product of the angle in radian measure subtended by the arc at the centre and the radius.

So l = theta r. Say theta is the angle subtended by the arc at the centre.

Therefrom, r = l / Theta.

Q: How do you find radius when arc length is given?

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you need to know the formula the arc length is equal to the radius times the angle made by the length of arc s = r(theta) s=arc length r=radius theta=angle

Length = angle˚/360˚ x 2∏r

The length of the arc is r*theta where r is the radius and theta the angle subtended by the arc at the centre of the circle. If you do not know theta (or cannot derive it), you cannot find the length of the arc.

The radius is a cord, is it not?

You can use the cosine rule and the three lengths of the triangle to find the central angle X, (in radians). Then the length of the arc is r*X units.

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you will need to know the angle subtended by the arc; arc length = radius x angle in radians

(arc length / (radius * 2 * pi)) * 360 = angle

you need to know the formula the arc length is equal to the radius times the angle made by the length of arc s = r(theta) s=arc length r=radius theta=angle

With the information given, you cannot. You need the radius or the central angle.

Length = angle˚/360˚ x 2∏r

The length of the arc is r*theta where r is the radius and theta the angle subtended by the arc at the centre of the circle. If you do not know theta (or cannot derive it), you cannot find the length of the arc.

You also need the measure of the central angle because arc length/2pi*r=measure of central angle/360.

You can use the cosine rule and the three lengths of the triangle to find the central angle X, (in radians). Then the length of the arc is r*X units.

The radius is a cord, is it not?

To find the arc length given the radius and angle measure in degrees, you must first convert the angle from degrees to radians, using the formula: Degrees = Radians X (pi/180). Then take the radians and the radius that you are given, and put them into the formula of Q = (a/r) where Q is the angle in radians, a is the arc length, and r is the radius. When you have this, simple multiply both sides by the radius to isolate the a. Once you do this, you have your answer.

the formula for the arc of a triangle is the arc length is equal to the angle times the radius. s=arc length theta=angle made y length of the arc lenth r=radius s=theta times radius

multiply the chord length and radius and divide by 2