Question

In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the arc cut off by the angle?

Answer 1

Given the radius, circumference can be solved by the equation, C = 2πr. The circumference of the circle above is C = 2π(8 in) = 16π in. To solve for the length of the segment joining the arc is the circumference times the ratio of central angle and 360 degrees.

Length of the segment = (16π in)(60/360) = 8/3 π in

Thus, the length of the segment is approximately 8.36 in.

Answer 2

The length of segment joining the endpoints of the arc is
`8\ in`

Explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

`AC=BC` -----> is the radius of the circle

`m<CAB=m<CBA`

`m<ACB=60\°` ----> given problem (central angle)

Initially the triangle ABC is an isosceles triangle

Remember that

the sum of the internal angles of triangle must be equal to
`180\°`

For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to
`60\°`

The equilateral triangle has three equal sides and tree equal angles

so

`AC=BC=AB`

Hence

The length of segment joining the endpoints of the arc is
`8\ in`