Question

a circular arc of length 16 feet subtends a central angle of 65 degrees. find the radius of the circle in feet. (note: you can enter π as 'pi' in your answer.)

Answer 1

Let's start with the formula for the length of a circular arc:

length of arc = (central angle/360 degrees) x 2 x pi x radius

We are given that the length of the arc is 16 feet and the central angle is 65 degrees. We need to find the radius of the circle.

Substituting the given values into the formula, we get:

16 = (65/360) x 2 x pi x radius

Simplifying the right-hand side, we get:

16 = 0.18056 x pi x radius

Dividing both sides by 0.18056 x pi, we get:

radius = 16 / (0.18056 x pi)

Simplifying the right-hand side, we get:

radius = 28.283 feet (rounded to three decimal places)

Therefore, the radius of the circle is approximately 28.283 feet.