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GalinKa [24]
3 years ago
10

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?

Mathematics
2 answers:
kaheart [24]3 years ago
7 0

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



g100num [7]3 years ago
3 0
Given the radius, circumference can be solved by the equation, C = 2πr. The circumference of the circle above is C = 2π(8 in) = 16<span>π 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 = (16</span>π in)(60/360) = 8/3 <span>π in

Thus, the length of the segment is approximately 8.36 in. </span>
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