My Math Forum Help with Arcs

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 May 3rd, 2019, 07:23 AM #1 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 Help with Arcs Hello, I dont know if this goes in Geometry or Trigonometry, so bear with me. I would like some help with a math experiment I am doing. You know me, I love to experiment. Here is the problem. Imagine a perfect circle. The radius is 1. Now, divide the circle into six equal triangles. You now have six triangles with equal sides and angles, with an arc on one side. Obviously, 2*Pi*r, (r being 1,) is 6.283185307...... Divide that by six, because you divided the circle in six, the arc length would be 1.047197551.... Here is the experiment: If you had the arc, and the base, which is 1, and the angles the arc hit the base, which are 30 degrees each, How would you find the length of the arc? Any help with this will be appreciated, Jared
 May 3rd, 2019, 08:25 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,036 Thanks: 2274 Haven't you just found the arc lengths? They're twice the given angle (in radians).
 May 3rd, 2019, 10:54 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,036 Thanks: 2274 If the given angle, in radians, is θ, the arc length is θ/sin(θ). For the angle you gave, sin(θ) = 1/2, so the arc length is 2θ.
 May 4th, 2019, 09:26 AM #5 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 @skipjack, thank you so much. I had no idea there was an easier way to find it then my complicated equation experiment. Still, it was quite fun coming up with it and figuring it out on my own and getting the same answer. Thanks so much for teaching me. Happy calculating, Jared

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