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How do you find length of arc knowing only the chord of arc and radius?
Wiki User
∙ 14y ago
Well, drawing out the diagram; you should have one triangle with all 3 sides with values. Lets call the radius 'r' , the chord length 'c' and the arc length 'a'. Your triangle should have two sides labelled each as 'r', and 'c'should be the last side.
Firstly, we know that the rule for the arc length is radius x theta (radians).
So we need a theta. To find theta, we can use the cosine rule, since we have all 3 sides and no angle.
The cosine rule is a^2=b^2+c^2-2bcCosA. We can transpose this into: CosA=(b^2+c^2-a^2)/2bc.
If we sub in our 'c' as the 'a' in the rule above and the two 'r's as 'b' and 'c', we get our new rule as CosC=(r^2+r^2-c^2)/2rr. We can then simplify that to be CosC = (2r^2-c^2)/2r^2. After that, inverse cosine the value and you should get angle C.
Finally sub in your values into the arc length rule: radius x theta, and you should get your answer.
P.S. Make sure your calculator is in radians.
Wiki User
∙ 14y ago
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How do you find the measure of an arc knowing only the chord of arc and radius?
you have a triangle formed by the radius on 2 and the chord on the other. the angle in that triangle that is opposite the chord, find its measure in radians take that measure (in radians) and multiply it by the radius to get the arc length
How do you find the chord length with the central angle and radius?
If the central angle is 70 and the radius is 8cm, how do you find out the chord lenght?
How do you find the radius of a circle if you know the length of a chord is 4 cm length?
Unless the chord is the diameter, there is no way to measure the radius of the circle. This is because the radius is in no way dependent on chord length since circles have infinite amount of chord lengths.
How do you find a chord length with the central angle and radius given?
If the radius is 8cm and the central angle is 70, how do yu workout the chord lenght?
How do you find radius of a circle if cord length is given?
The longest chord in a circle is its diameter and halve of this is its radius.
How do you find the measure of an arc knowing only the chord of arc and radius?
you have a triangle formed by the radius on 2 and the chord on the other. the angle in that triangle that is opposite the chord, find its measure in radians take that measure (in radians) and multiply it by the radius to get the arc length
How do you Find Arc Length of Segment from Chord Length and Radius?
multiply the chord length and radius and divide by 2
How do you find the radius given the chord length?
If you are given a chord length of a circle, unless you are given more information about the chord, you can not determine what the radius of the circle will be. This is because the chord length in a circle can vary from a length of (essentially) 0, up to a length of double the radius (the diameter). The best you can say about the radius if given the chord length, is that the length of the radius is at least as long has half half the chord length.
How do you find the chord length with the central angle and radius?
If the central angle is 70 and the radius is 8cm, how do you find out the chord lenght?
How do you find the radius of a circle if you know the length of a chord is 4 cm length?
Unless the chord is the diameter, there is no way to measure the radius of the circle. This is because the radius is in no way dependent on chord length since circles have infinite amount of chord lengths.
How do you find a chord length with the central angle and radius given?
If the radius is 8cm and the central angle is 70, how do yu workout the chord lenght?
How do you find radius of a circle if cord length is given?
The longest chord in a circle is its diameter and halve of this is its radius.
What is the formula to calculate the radius of a segment knowing the height of the segment and cord length?
Assume that the height of the segment is h, the chord length is c and the radius is r then: r2=(r-h)2+(c/2)2 (We join two radii to the two ends of the chord then extend the height of the segment to the center of the circle in which the segment is inscribed so this height will bisect the chord and you use the pythagorean theorem to find the radius)
Find chord length with radius and arc length known?
r = known radius x = known arc length --------------------------- C (circumference of circle) = 2 * PI * r A (angle of chord in degrees) = x / C * 360 L (length of chord) = r * sin(A/2) * 2
How do you find the radius of a cone knowing only side length?
You cannot.
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
How do you find the radius of a circle if you know the length of a chord and the shortest distance from the center of the chord to the circle?
Imagine if you will a circle with a chord drawn through it and a line running from the center of that chord to the center of the circle. That line is necessarily perpendicular to the chord. This means you have a right triangle whose hypotenuse is the radius of the circle. The radius is thus given by: r = sqrt{(1/2 chord length)^2 + (length of perpendicular line)^2} The actual formula to find the radius is as follows: r= C squared/8a + a/2, where C is the chord length, and a is the distance from center point of the chord to the circle , and a and C form an angle of 90 degrees. the entire formula before simplification is r = sqrt {(1/2 C)^2 + (r-a)^2}
