TopAnswer to question how to solve the value of radius given the angle and arc length, is shown below with help of steps:

Step 1: First, we calculate center angle of given Geometry, which is generally given in question like we have a Circle geometry, whose center angle is 60 degree.

Step 2: After center angle of given geometry, we calculate arc length of given geometry, which is also given in question like Arc Length of Circle geometry is 7.33 inch.

Step 3: After first two steps, we use following formula for evaluation of Radius of Circle.

Arc length of geometry (s) = radius of geometry (r) * center angle of geometry (θ).

= > radius of geometry (r) = Arc length of geometry (s) / center angle of geometry (θ).

We take an example, which define whole process for calculation of radius of given geometry –

Example: An arc length of circle is 8.33 inch and center angle of circle is 120 degree, then find the radius of given circle?

Solution: we use following steps for evaluating the radius of given circle–

Step 1: Firstly, we calculate center angle of given geometry, here center angle of circle is 120 degree. So, center angle of circle (θ) = 120 degree = (2 * Π) / 3 = 2.09 radian.

Step 2: After center angle of given geometry, now we calculate arc length of given geometry, here arc length of circle geometry is 8.33 inch.

Step 3: After first two steps, we use following formula for evaluation of radius of circle –

Arc length of circle (s) = radius of circle (r) * center angle of circle (θ),

=> Radius of circle (r) = Arc length of circle (s) / center angle of circle (θ),

=> Radius of circle (r) = 8.33 / 2.09,

=> r = 3.98 inch,

So, radius of circle is 3.98 inch.