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 \(8\ in\)
