So, I have an arc that's part of a circle that I must "travel across".The circle has a radius of 15 - a circumference of 94.248 (rounding). The arc length in question is equal to 15.708.Now, normally, you could sort of walk along the arc, turning with it. But, if I could only travel straight, I need to know how I would get from one part of the arc to 15.708 units later in the arc of the circle (only being able to travel straight, or make 90 degree turns).

Question

So, I have an arc that&#039;s part of a circle that I must &quot;travel across&quot;.The circle has a radius of 15 - a circumference of 94.248 (rounding). The arc length in question is equal to 15.708.Now, normally, you could sort of walk along the arc, turning with it. But, if I could only travel straight, I need to know how I would get from one part of the arc to 15.708 units later in the arc of the circle (only being able to travel straight, or make 90 degree turns).

svirajueh · Accepted Answer

For a thousand years, the only extensive trigonometric table was about precisely this question:  Ptolemy&#039;s table of chords.If the central angle is   θ and the diameter is   d, then the length of the chord is   d  sin  ⁡  (  θ      /    2  ).Observe that             15.708      94.248        =            1      6      , so the central angle is       60    ∘  . For a       60    ∘   angle, the length of the chord is exactly the radius.

So, I have an arc that's part of a circle that I must "travel across". The circle has a radius

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