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A wire of length 20cm is bent so as form arc of circle of radius 12cm what is the angle subtended at the center in radians is?
Wiki User
∙ 13y ago
When the angle is measured in radians
arc_length = angle x radius.
So,
20cm = angle x 12cm
=> angle = 20cm / 12cm
~= 1.67 radians
Wiki User
∙ 13y ago
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When a body moves along a semicircle total angle subtended by it at centre of circle is?
Pie/2=22/7/2Angle in radians =Total length of the arc/radius of the circle
What is radian measure?
A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle, approximately 57°17'44.6"
How do you find radius of a circle if given arc length?
you will need to know the angle subtended by the arc; arc length = radius x angle in radians
An arc of a circle that is 6Cm in length intercepts a central angle of 1.5 radians find the number of Cm in the radius of the circle?
An arc of length 6cm subtending an angle at the centre of 1.5c is equivalent to the whole circle of length 2πr subtending 2π radians. Therefore, 6/1.5 = 2πr/2π = r : Then r = 4 cm. NOTE : A radian can be defined as the angle at the centre of a circle subtended by an arc equal in length to the radius. So an arc subtending an angle of 2 radians is twice the length of the radius. An arc subtending an angle of 1.5 radians is thus 11/2 times as long as the radius.
What is the relationship between the chord and the radius of circle?
The relationship between the chord and the radius of the circle is Length of the chord = 2r sin(c/2) where r = radius of the circle and c = angle subtended at the center by the chord
When a body moves along a semicircle total angle subtended by it at centre of circle is?
Pie/2=22/7/2Angle in radians =Total length of the arc/radius of the circle
What is radian measure?
A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle, approximately 57°17'44.6"
How do you find radius of a circle if given arc length?
you will need to know the angle subtended by the arc; arc length = radius x angle in radians
What is the name for 90 degrees in the circle?
If an arc of a circle is drawn so that the length of the arc is equal to the radius of the circle then the angle at the centre of the circle subtended by the arc is called one radian.Then the angle subtended by the entire circle is given by the ratio , circumference / radius = 2πr/r = 2π radians.2π radians is equivalent to 360°So, π radians = 180°and thus, π/2 radians = 90°Pi over two, or Pi divided by two radians is the name for 90° in a circle.
What is the length of arc subtended by a central angle of 101.6 degrees in a circle with a diameter of 219 feet?
101.6 degrees = 1.7733 radians. So arc = radius*angle (in radians) = 219/2*1.7733 = 194.2 ft.
If you have a Radian of 65 and a radius of 5 what is the length of the arc?
The length of an arc subtending an angle of x radians ir r*x. Here the angle subtended is 65 radians so the length of the arc is 5*65 = 325 units (slightly more than 10 times round the circle).
An arc of a circle that is 6Cm in length intercepts a central angle of 1.5 radians find the number of Cm in the radius of the circle?
An arc of length 6cm subtending an angle at the centre of 1.5c is equivalent to the whole circle of length 2πr subtending 2π radians. Therefore, 6/1.5 = 2πr/2π = r : Then r = 4 cm. NOTE : A radian can be defined as the angle at the centre of a circle subtended by an arc equal in length to the radius. So an arc subtending an angle of 2 radians is twice the length of the radius. An arc subtending an angle of 1.5 radians is thus 11/2 times as long as the radius.
How to find length of arc if radius and angle subtended at the center are given?
Full circumference of the circle = (2 pi) times (radius)Arc is a fraction of the full circumference.The fraction is (angle subtended at the center) divided by (360 degrees).If you have the radius 'R' and the angle 'A', the length of the arc is(pi) (R) (A) / 180
The ratio of the arc length to the radius?
The arc_length is given by the angle measured in radians times the radius of the arc. To convert degrees to radians divide by 180° and multiply by π radians. eg 45° = 45° ÷ 180° × π radians = π/4 radians. eg 60° = 60° ÷ 180° × π radians = π/3 radians.
A chord of a circle of radius 5cm subtends the length of 80 degree at the center of the circle find the length of the chord?
The length of a chord = pi*r*x/180 where x is the angle subtended. = pi*5*80/180 = 6.98 cm
What is the relationship between the chord and the radius of circle?
The relationship between the chord and the radius of the circle is Length of the chord = 2r sin(c/2) where r = radius of the circle and c = angle subtended at the center by the chord
Why radian has no dimension?
The simplest explanation is that a radian is defined as the distance an angle would subtend along the circumference of a circle of radius "r" divided by the radius "r." If we call the subtended arc "a," then both "r" and "a" are measured in length units, which of course cancel out when the ratio "a" over "r" is taken.The easiest way to understand this is probably through an example. Take an angle of 30 degrees. If we construct a unit circle (radius = 1 unit) centered at the vertex of the angle, then we know the circumference of the circle is 2(pi)r = 6.283 units. We also know that the circumference of the circle is 360 degrees by definition, so a 30 degree angle subtends 30/360, or 8.3 percent of the circumference of 6.283 units, or 0.524 units. Thus, the angle in radians is the length of the subtended arc, 0.524 units, over the length of the radius, 1 unit, or 0.524 units/1 unit = 0.524 (with the units dimension canceling out).Since by definition, circumference = 2(pi)(r) = 360 degrees, it is easy to see that an arc of "r" units (that is one radian) = 360/(2(pi)) = 57.3 degrees and that there are 2(pi), or 6.28 radians in 360 degrees. If one radian = 57.3 degrees, then the 30 degree example above should equate to 30/57.3 = 0.524 radians, just as was shown.Bottom line is that an angle in radians defines a given subtended arc distance for a circle of any radius measured in any units, as long as it is centered at the vertex of the angle. If a circle of radius 57 hoozits is centered at the vertex, then an arc of length "57 times the angle in radians" hoozits is subtended. Similarly, if a circle of radius 23 cm is centered at the vertex, then an arc of length "23 times the angle in radians" cm subtended. In either case, the subtended angle in degrees is the angle in radians times 360/((2)(pi)).
