How to determine the arc length in Excel?

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Guest

In a 60 degree right triangle, x-axis = 1 and y-axis = Sqrt(3).
In degree mode, Tan(60) = Sqrt(3).
In radian mode, Tan(60 x Pi / 180) = Sqrt(3)
60 x Pi / 180 is the arc length between 60 degree angle.
Therefore, there is a direct relationship between arc length and x & y
length for each triangle.
Given with any x and y lengths for a right triangle, I would like to
determine the arc length based on this relationship.
Does anyone have any suggestions on how to determine the formula to
calculate the arc length?
In this example, x =1 in cell A1 and y = Sqrt(3) in cell B1, I would like to
determine the arc length = Pi / 3 in cell C1.
Does anyone have any suggestions?
Thanks in advance for any suggestions
Eric
 
First, your geometry is a little off. A true arc length both points should
lie on the circle which means X & Y should both be the same length. With a
right triangle If X if on the circle, Y will extend out past the circle. If
Y is on the circle, X will be inside the circle and you would have to extend
X to intersect the circle.

Arc length is the circumference times (angle of arc/360)
circumference = 2 *pi*radius

Your case where X is on the circle
Radius is X
circumference = 2 * pi * X
angle of arc (radians) = tan(Y/X)
angle of arc (degrees) = (pi/180) * tan(Y/X)

Arc Length = (2 * pi * X) * (pi/180) * tan(Y/X)

The answer could also be if Y is on the circle

Arc Length = (2 * pi * Y) * (pi/180) * tan(Y/X)
 
This should work although I am sure there is a way to simplify it.

=DEGREES(ATAN(B1/A1)*SQRT(A1^2+B1^2)*(PI()/180))

HTH
Martin
 
My last posting I had Tan instead of ATan

First, your geometry is a little off. A true arc length both points should
lie on the circle which means X & Y should both be the same length. With a
right triangle If X if on the circle, Y will extend out past the circle. If
Y is on the circle, X will be inside the circle and you would have to extend
X to intersect the circle.

Arc length is the circumference times (angle of arc -degrees/360)
or
Arc length is the circumference times (angle of arc-radians/2 * pi)
circumference = 2 *pi*radius

Your case where X is on the circle
Radius is X
circumference = 2 * pi * X
angle of arc (radians) = arctan(Y/X)

Arc Length = (2 * pi * X) * (Atan(Y/X)/ (2 * pi)
Arc Length = X * Atan(Y/X)

The answer could also be if Y is on the circle

Arc Length = Y * Atan(Y/X)

Martin solution doesn't make sense
=DEGREES(ATAN(B1/A1)*SQRT(A1^2+B1^2)*(PI()/180))

A and B would be the legs of the triangle. You have one leg and the
hypotenuse
it should of been
 
If the X and Y values are a co-ordinate then the circle through
that point has a radius of the hypotenuese of that triangle.
My formula calculates the arc length of that circle
back to the baseline.

I have no idea what the OP is trying to achieve but it
seems from his post that is the value that he requires.

Regards
Martin
 
Thank eveyone for suggestions
Eric

MartinW said:
This should work although I am sure there is a way to simplify it.

=DEGREES(ATAN(B1/A1)*SQRT(A1^2+B1^2)*(PI()/180))

HTH
Martin
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