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 ar
c cut off by the angle?
2 answers:
Answer:
The length of segment joining the endpoints of the arc is
Step-by-step explanation:
we know that
In the triangle ABC
see the attached figure to better understand the problem
-----> is the radius of the circle
----> 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
For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to
The equilateral triangle has three equal sides and tree equal angles
so
Hence
The length of segment joining the endpoints of the arc is
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