Since the minor arc is 30 degrees, the major arc is 330 degrees (360 - 30).
So we have:
330 degrees : arc length 10
30 degrees : arc length x
330/30 = 10/x
11/1 = 10/x
x = 10/11
x = 0.9 approximately
So the length of the minor arc is approximately 0.9 units.
If the radius of the circle is r units and the angle subtended by the arc at the centre is x radians, then the length of the arc is r*x units. If you are still working with angles measured in degrees, then the answer is r*pi*y/180 where the angle is y degrees. If r and x (or y) are not available, or cannot be deduced, then you cannot find the length of the arc.
"That would be A minor. Go a minor third below the tonic of the major scale to find the relative minor." Technically, there is no relative harmonic major to the key of C Major. The relative minor scale of C Major would the natural minor scale of A. A harmonic minor scale raises the 7th note of the scale a half step, giving us G#, which is not in the key of C Major.
Find the circumference of the whole circle and then multiply that length by 95/360.
Ursa major and USA minor
It is simply greater than 180 degrees but less than 360 degrees
13.08
find the arc length of minor arc 95 c= 18.84
5.23
I'm assuming that "c" is short for "circumference". The length of an arc is (circumference)*(360/angle). So the length of an arc in a circle with circumference length of 18.84 is 6782.4/angle, where the angle is measured in degrees.
Count up a sixth from the major (C) to find the minor (A).
If the radius of the circle is r units and the angle subtended by the arc at the centre is x radians, then the length of the arc is r*x units. If you are still working with angles measured in degrees, then the answer is r*pi*y/180 where the angle is y degrees. If r and x (or y) are not available, or cannot be deduced, then you cannot find the length of the arc.
How do you memorize relative minors? Learn the major scales (key signatures, sharps, and flats). Get accustomed to thinking of scale degrees simultaneously by note and number. To convert to relative minor, I find it easier to count backwards 8-7-6 (C-B-A) from the octave root (8th degree), and then add sharps or flats as I know them to be in the relative major. I play guitar so it's easy to recover from mistakes by using it as a chromatic approach or a slow bend.
An arc length of 120 degrees is 1/3 of the circumference of a circle
The relative key is the one with the same key signature. For C major, it's A minor.
"That would be A minor. Go a minor third below the tonic of the major scale to find the relative minor." Technically, there is no relative harmonic major to the key of C Major. The relative minor scale of C Major would the natural minor scale of A. A harmonic minor scale raises the 7th note of the scale a half step, giving us G#, which is not in the key of C Major.
In order to find length BC the length of AC or length of the hypotenuse must be given
Find the circumference of the whole circle and then multiply that length by 95/360.