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)


"Eric" wrote:

> 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

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


"Eric" <(E-Mail Removed)> wrote in message
news:0CD65ABA-6256-42A2-B1B0-(E-Mail Removed)...
> 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

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


"MartinW" wrote:

> 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
>
>
> "Eric" <(E-Mail Removed)> wrote in message
> news:0CD65ABA-6256-42A2-B1B0-(E-Mail Removed)...
> > 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
>
>
>

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


"Joel" <(E-Mail Removed)> wrote in message
news:BF79374F-8448-4CF8-BC87-(E-Mail Removed)...
> 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
>
>
> "MartinW" wrote:
>
>> 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
>>
>>
>> "Eric" <(E-Mail Removed)> wrote in message
>> news:0CD65ABA-6256-42A2-B1B0-(E-Mail Removed)...
>> > 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
>>
>>
>>

Thank eveyone for suggestions
Eric

"MartinW" wrote:

> 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
>
>
> "Eric" <(E-Mail Removed)> wrote in message
> news:0CD65ABA-6256-42A2-B1B0-(E-Mail Removed)...
> > 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
>
>
>