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

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  

$m$

$m$ ----> 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.