whats the formula for arc length???

Answer 1

Im assuming you are talking about a perfectly circular arc curve, a portion of a circle. And not some randomly curvy continuous curve plotted with some given polynomial.

For a arc formed from a circle-

The arc length is given by the fraction, F, of the full circle that forms the arc, multiplied by the length around the full circle, its circumference C:
C ⋅ F

That fraction of the full circle that forms the arc is the ratio of the angular measure of the arc to the angular measure of a full circle.
F = θ/360°

If the arc is only over 45°, then θ = 45°, then you are dealing with 45°/360° = 1/8 of a circle.

Take that ratio times the full distance around the circle, the circumference, to equal arc length.

So, in degrees, the arc length is:
C ⋅ θ/360°, where θ is the measure of the arc in degrees.

It works just the same in radian measure. The angle, θ, in radians, out of a possible 2π about the circle will yield the fraction of the cirlce θ/2π. The arc length is given by:
C ⋅ θ/2π, where θ is in radian measure.

Continuing along the same logic, with radian measure, you can expand the circumference, C, into 2⋅π⋅r (the equation for finding circumference from radius). This gives us:
2πr ⋅ θ/2π, which reduces:
r ⋅ θ, where θ is still in radians.

r ⋅ θ works because r represents the length of the radius and θ represents the "number of radii" on the surface of the circle that encompasses the angle.

Answer 2

Arc Length Formula

Answer 3

For arc length of a circle, the formula is (radians)x(radius) or (degrees)x(pi)/(180)x(radius)
For arc length of a line defined by f(x) using calculus, the equation is the integral of [ the square root of ( 1+the (derivative of the function)^2)]evaluated from lower bound to upper bound. The source gives it in real mathematical symbols

Answer 4

The easiest way to think about it is like a pie chart, the arc is a percentage of the circle, so calculate the percentage of 360 degrees that the arc length has, ie my arc goes 30 deg so thats 8.3% so that means that 1.083 times the circumference of the whole circle (2r* pi) will give you your arc length.

Answer 5

the formula is S=rѲ S- the arc length, r- radius Ѳ=central angle but should be express in radian π = 3.14 applying the formula, we have S=?, r=144 , Ѳ=260* π/180 hence, Ѳ=13π/9 S=(144)(13)(3.14)/9 --manipulating the equation S= 653.12 --answer, you the correct

Answer 6

Assuming a circular arc.

Circumference = 2*pi * radius: Theta = 2*pi
ArcLength= Radius * arcAngle: arc Angle in radians

ArcLength = Radius * arcAngle * pi/180 : arcAngle in degrees

Answer 7

Hello,

LET x = your angle for the arc.

Then the arc length is =( x/360)* 2PI

Hope This Helps!!

Answer 8

In a circle, for an arc of angle Θ the arc length is
a=2π*r*Θ/(2π)
a=rΘ where Θ is in radians.

Answer 9

radius * angle (measured in radians)

for degrees: r * theta * pi /180