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? 8 8√2 8√3

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Kstrong18 Kstrong18 · Answer 1 · 2017-06-04T00:29:37+02:00

The answer would be 8. An isosceles triangle is formed with each angle being 60, which means which side is 8.

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calculista calculista · Answer 2 · 2019-02-02T22:23:08+01:00

Answer:

The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]

Step-by-step explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

[tex]AC=BC[/tex] -----> is the radius of the circle

[tex]m<CAB=m<CBA[/tex]

[tex]m<ACB=60\°[/tex] ----> 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 [tex]180\°[/tex]

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

The equilateral triangle has three equal sides and tree equal angles

so

[tex]AC=BC=AB[/tex]

Hence

The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]