In a circle, the number of radians of the center angle of an arc with an arc length equal to 3 times the root of the radius is

In a circle, the number of radians of the center angle of an arc with an arc length equal to 3 times the root of the radius is

The arc length is equal to the radius multiplied by radians, so radians = 3 ^ (1 / 2)

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．

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 arc length of a circle is equal to the variable length of the circumscribed equilateral triangle of the circle, the radian number of the arc length to the center angle of the circle is

Let the circle radius be r, then the side length of circumscribed regular triangle is 2 √ 3R
Then the arc length is also 2 √ 3R, and the radian of the corresponding center angle is 2 √ 3 rad

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．

In a circle with radius r, the center angle of the arc with arc length of 3 π R / 4 =? radian

This is using the arc length formula L= α* r
In a circle with radius r, the center angle of the arc with arc length of 3 π R / 4 = (3 π R / 4) / r = 3 π / 4 radians