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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 an arc is equal to the side length of the inscribed positive triangle of the circle in which it is located, the number of radians of the center angle of the arc is How is this possible? How can the shortest straight line between two points be as long as a curve? Please explain!
The starting point and ending point of the arc are not two points of one side of the triangle
If the length of an arc of a circle is equal to the length of one side of the inscribed regular triangle of the circle, then the center angle of the arc is____ Radians?
a/sin60=2r
a=2rsin60=√3r
Arc length = R α
α= √ 3R / r = √ 3 radians
If the radius of the circle becomes 3 times of the original and the length of the arc remains unchanged, the central angle of the arc is several times of the central angle of the original arc
If the radius of the circle becomes 3 times of the original and the length of the arc remains unchanged, the central angle of the arc is (1 / 3) of the central angle of the original arc
Center angle (radian) = arc length ÷ radius
So it became 1 / 3 of the original
Hope to adopt those who don't understand. Welcome to ask questions
Given that the radius of the circle is r, what radians is the center angle of the arc with arc length of 3R / 4?
According to the proportion, the radian corresponding to the circle with radius R is 2 rows, and the center angle of the arc with radius 3R / 4 is 2 rows multiplied by 3 / 4 to get 3 / 2 rows
Calculation formula of arc radian
α = L / r = 2S / (R ＾ 2) Note: α Is radian, l is arc length, R is radius and S is arc area
RELATED INFORMATIONS
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