[Main General Bulletin Board | BBFAQ | Prev by Date | Next by Date | Post Followup ] Member Login / Signup - Members see fewer ads. - Latest Member Gallery Photos Here's my attempt to "show work" Like This Post: - Subscribe to Daily Digest for this Bulletin Board Posted by IrieTom [Email] (#1032) [Profile/Gallery] (more from IrieTom) on Fri, 19 Nov 2004 10:11:44 In Reply to: 10" x (the square root of 3), or ~17.32", IrieTom [Profile/Gallery] , Thu, 18 Nov 2004 13:37:03 Alert me when someone posts in this thread: Members do not see ads below this line. - Help Keep This Site Online - Signup

Picture the circle as a clock face, with an equilateral triangle inscribed inside where the corners of the triangle are at 12 o'clock, 4 o'clock, and 8 o'clock. Now draw a line from the exact center of the circle (also the exact center of the triangle) to 4 o'clock and 8 o'clock. This produces a smaller triangle with angles of 30, 30, and 120 degrees. One last line from the center towards 6 o'clock will divide this smaller triangle in half, leaving two 30-60-90 degree triangles.

It has been proven in geometry that the sides of a 30-60-90 triangle are proportional to x (opposite the 30 degree angle), 2x (opposite the 90), and [sqrt 3]x (opposite the 60). In our case, the 2x side is equal to 10 (the radius of the circle), so we can solve for x, which is 5. Therefore, the bottom edge of this small triangle is equal to 5 times [sqrt 3]. This is equal to half of one side of the equilateral triangle, so doubling this gives us 10 times [sqrt]3.

posted by 24.195.59...

• if you passed high school geometry read on..., Liam, Thu, 18 Nov 2004 12:56:10
  • Here's another solution..., zeke, Sat, 20 Nov 2004 17:28:54
  • So, the question remains....>>>, PGAero , Thu, 18 Nov 2004 16:34:40
    • Re: So, the question remains....>>>, Liam, Thu, 18 Nov 2004 20:09:32
      • questions to ask:, IrieTom , Thu, 18 Nov 2004 23:54:15
  • Re: if you passed high school geometry read on..., Liam, Thu, 18 Nov 2004 16:11:03
  • 10" x (the square root of 3), or ~17.32", IrieTom , Thu, 18 Nov 2004 13:37:03
    • Here's my attempt to "show work", IrieTom , Fri, 19 Nov 2004 10:11:44 <-- Viewing This Message
      • Sorry, "no name" is me...........nm, zeke, Fri, 19 Nov 2004 14:33:24
  • Re: if you passed high school geometry read on..., Gene N , Thu, 18 Nov 2004 13:35:29
    • Re: if you passed high school geometry read on..., Aero'ed, Thu, 18 Nov 2004 18:54:27
      • I think what he did was this..., zeke, Fri, 19 Nov 2004 04:36:03
        • ahh, as simple as it gets n/m, Aero'ed, Fri, 19 Nov 2004 09:17:00
    • Re: if you passed high school geometry read on..., MO, Thu, 18 Nov 2004 14:11:08
    • We get the same result but you must have.., zeke, Thu, 18 Nov 2004 14:09:35
  • There's only one equilateral triangle that can be..., zeke, Thu, 18 Nov 2004 13:35:00
    • Re: There's only one equilateral triangle that can be.., MO, Thu, 18 Nov 2004 14:11:03
      • The hypotenuse is twice the short leg...., zeke, Thu, 18 Nov 2004 14:37:53
  • Re: square that diameter and 1/2? n/m, t_mokes, Thu, 18 Nov 2004 13:11:35

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