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

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

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.