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What is the measure of a central angle of a circle whose rays subtend an arc on the circle whose length is equal to the radius of the circle?
Wiki User
∙ 12y ago
Arc Length = (x/360)2pi*r
As given in the question The radius and the arc length are the same value.
So substituting
r = (x/360)2pi*r
Algebraically rearrange
r/r = (x/360)2pi
Cancel down 'r'
Hence
1 = (x/360)2pi
Now since 360 degrees = 2 pi radians
Substitute again
1 =( x / 2pi) 2 pi
Cancel down by '2 pi'
Hence x = 1 radian.
To convert radians to degrees. Remember
180 degrees = pi(3.141592.... radians)
So dividing 180 /3.141592... =57.29577951.... degrees. The answer!!!!
lenpollock
Wiki User
∙ 12y ago180/π=57.27270
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What is the formula for calculating the arc length?
For a circle: Arc Length= R*((2*P*A)/(360)) R being radius, P being pi (3.14159), and A being the measure of the central angle.
What is the measure of the central angle of a circle with the arc length of 29.21 and the circumference of 40.44?
arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.
How can you measure the length of an arc in a circle?
by sucking dick
How can the radian measure of an angle determine the arc length on the unit circle?
The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.
How do you find the center of a semicircle?
measure the length of the circle and divide it by 6
How do you find the degree measure of a central angle in a circle if both the radius and the length of the intercepted arc are known?
-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees
How do you find the arc length with the angle given?
An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length. (measure of central angle/360 degrees) = (arc length/circumference) arc length = (measure of central angle/360 degrees)(circumference) But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
What is the length of an arc of a circle?
The length of an arc of a circle refers to the product of the central angle and the radius of the circle.
What is the formula of a central angle of a circle?
Central angle of a circle is the same as the measure of the intercepted arc. davids1: more importantly the formulae for a central angle is π=pi, R=radius Central Angle= Arc Length x 180 / π x R
What is the measure of the arc of a circle intercepted by a central angle that measures 64 degrees?
64°/360° = 8/45 of the circle = 0.1777 (rounded, repeating)The arc's length is 8/45 of the circle's total circumference.
How do you work out the circumference of a circle using radius?
The formula for calculating the circumference of a circle is 2πr, where r is the radius of the circle and π is 3.1415926535890793 - usually shorted to either 3.1416 or 3.14 So that the circumference of a circle with a radius of 10 units is 62.83 units There are pi radians in a half of a circle. Thus, the measure of a central angle which is a straight line is pi radians. We have a formula that show that the length of an intercepted arc is equal to the product of the angle in radians that intercepts that arc, with the length of the radius of the circle. So we can say that the length of a semicircle is (pi)(r). In a full circle are 2pi radians. So the length of intercepted arc from a central angle with measure 2pi is 2(pi)(r).
What is the radian measure of the central angle of a circle of radius 18 feet that intercepts an arc of length 10 ft?
It is 10/18 = 0.55... radians.
What does the diameter of a circle measure?
The length across the circle. 2 x the radius.
Find the lenght of a chord that cuts off an arc of measure 60 degrees in a circle of radius 12?
The radial length equals the chord length at a central angle of 60 degrees.
What is the formula for calculating the arc length?
For a circle: Arc Length= R*((2*P*A)/(360)) R being radius, P being pi (3.14159), and A being the measure of the central angle.
How can you measure the length of an arc in a circle?
by sucking dick
What is the measure of the central angle of a circle with the arc length of 29.21 and the circumference of 40.44?
arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.
