Question

How to work this out? 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

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`

Answer 2

The segment joining the endpoints of the arc cut off by the angle is 8 inches long. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.