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It is known that the arc length of an arc is equal to the side length of the inscribed regular triangle of its circle, then the radian number of the center angle of the arc is __
As shown in the figure,
△ ABC is an inscribed regular triangle of ⊙ o with radius r,
Then BC = 2CD = 2rsin π
3=
3r，
Let the number of radians of the center angle of the arc be α，
Then R α=
3r，
Solution α＝
3．
So the answer is:
3．
If the length of the arc is equal to the side length of the inscribed regular triangle of the circle, what are the radians of the center angle of the arc?
The radian is D and the radius of the circle is r
D = R three times the root sign
Circumferential length C = 2 π R
Angle = 2 π times (d divided by C) = root three
An arc is 12.5 cm long and its circumference is 200 cm. Find the degree of the center angle of the arc
（180 × 12.5）÷[3.14 × （200÷3.14÷2）]，
=2250÷100，
=22.5 (degrees),
Answer: the central angle of the arc is 22.5 degrees
If the length of an arc on a circle is equal to the length of the diameter of the circle, the degree of the center angle of the arc is degrees
Diameter D, arc length = D
Circumference = π D
Arc length / circumference = D / π d = 1 / π
Center angle of arc = (1 / π) * 360 = 114.59156 degrees
Note here that 1 / π is a ratio, independent of the angle, or it will be confused
The radius of the circle where an arc is located is 12 cm, and the arc length is 12.56 cm. Find the degree of the center angle of the circle opposite to the arc
Circumference of circle = π * 12 * 12 = 452.16 (cm2)
Center angle corresponding to circular arc: 12.56 / 452.16 * 360 ° ≈ 10 °
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In a circle, if the length of an arc is 2 / 5 of the circumference of the circle, find the degree of the center angle of the arc
three hundred and sixty × 2 / 5 = 144 °
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