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 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.

Answer 2

Answer:

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

Step-by-step 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 $8\ in$