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It is 10/18 = 0.55... radians.

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Q: What is the radian measure of the central angle of a circle of radius 18 feet that intercepts an arc of length 10 ft?
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What is the relation between the arc length and angle for a sector of a circle?

A sector is the area enclosed by two radii of a circle and their intercepted arc, and the angle that is formed by these radii, is called a central angle. A central angle is measured by its intercepted arc. It has the same number of degrees as the arc it intercepts. For example, a central angle which is a right angle intercepts a 90 degrees arc; a 30 degrees central angle intercepts a 30 degrees arc, and a central angle which is a straight angle intercepts a semicircle of 180 degrees. Whereas, an inscribed angle is an angle whose vertex is on the circle and whose sides are chords. An inscribed angle is also measured by its intercepted arc. But, it has one half of the number of degrees of the arc it intercepts. For example, an inscribed angle which is a right angle intercepts a 180 degrees arc. So, we can say that an angle inscribed in a semicircle is a right angle; a 30 degrees inscribed angle intercepts a 60 degrees arc. In the same or congruent circles, congruent inscribed angles have congruent intercepted arcs.


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.


If the radius of a circle is doubled how is the length of the arc intercepted by a fixed central angle changed?

If the radius of a circle is tripled, how is the length of the arc intercepted by a fixed central angle changed?


If the arc on a particular circle has an arc length of 12 inches and the circumference of the circle is 48 inches what is the angle measure of the arc?

The angle measure is: 90.01 degrees


If a circle has a central angle of 75 degrees that intercepts an arc of length 75 feet the number of feet in the radius is?

l= rθ Here θ = 75 * π/180 (Converting degrees into radian) r= l/θ = 75/ 75/180 π = 180/π = 57.3 approximately.

Related questions

A central angle of a circle of radius 30 cm intercepts an arc of 6 cm Express the central angle in radians and in degrees?

A central angle is measured by its intercepted arc. Let's denote the length of the intercepted arc with s, and the length of the radius r. So, s = 6 cm and r = 30 cm. When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian. To find the angle in our problem we use the following relationship: measure of an angle in radians = (length of the intercepted arc)/(length of the radius) measure of our angle = s/r = 6/30 = 1/5 radians. Now, we need to convert this measure angle in radians to degrees. Since pi radians = 180 degrees, then 1 radians = 180/pi degrees, so: 1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.


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).


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


Can you measure a line even though it goes on forever?

You cannot measure its length but you can measure its slope and intercepts.


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 relation between the arc length and angle for a sector of a circle?

A sector is the area enclosed by two radii of a circle and their intercepted arc, and the angle that is formed by these radii, is called a central angle. A central angle is measured by its intercepted arc. It has the same number of degrees as the arc it intercepts. For example, a central angle which is a right angle intercepts a 90 degrees arc; a 30 degrees central angle intercepts a 30 degrees arc, and a central angle which is a straight angle intercepts a semicircle of 180 degrees. Whereas, an inscribed angle is an angle whose vertex is on the circle and whose sides are chords. An inscribed angle is also measured by its intercepted arc. But, it has one half of the number of degrees of the arc it intercepts. For example, an inscribed angle which is a right angle intercepts a 180 degrees arc. So, we can say that an angle inscribed in a semicircle is a right angle; a 30 degrees inscribed angle intercepts a 60 degrees arc. In the same or congruent circles, congruent inscribed angles have congruent intercepted arcs.


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.


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.