Results 1 to 6 of 6
Thread: Using geometry....

20130420, 19:35 #1
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,859
 Thanks
 146
 Thanked 728 Times in 662 Posts
Using geometry...
....find the length of the side of a perfect octagon which has a measurement from its center to the perpendicular side of 8.
octagon.jpgLast edited by Maudibe; 20130809 at 04:27.

20130422, 08:25 #2
 Join Date
 Dec 2009
 Location
 Oxfordshire, UK
 Posts
 1,972
 Thanks
 158
 Thanked 184 Times in 177 Posts
6.6 to one decimal place?

20130422, 23:23 #3
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,859
 Thanks
 146
 Thanked 728 Times in 662 Posts
The answer is correct! You might have calculated the answer using the tangent which is an acceptable method, however, without using tangent, sin, or cosin, could you still logically solve it?
Last edited by Maudibe; 20130422 at 23:55.

20130423, 04:05 #4
 Join Date
 Dec 2009
 Location
 Oxfordshire, UK
 Posts
 1,972
 Thanks
 158
 Thanked 184 Times in 177 Posts
I did indeed use tan  and there's no way I would have thought of any other way! My maths courses were a long time ago  I thought I did well thinking of the tan method!

20130423, 12:12 #5
 Join Date
 Aug 2010
 Location
 Pa, USA
 Posts
 2,859
 Thanks
 146
 Thanked 728 Times in 662 Posts
...And you sure did. Every time I use them with angles, I have to take a quick refresher course.

20130427, 19:32 #6
 Join Date
 Jan 2001
 Location
 La Jolla, CA
 Posts
 1,546
 Thanks
 39
 Thanked 69 Times in 65 Posts
You could approximate the side without trig since the triangle formed by the 8, the bisected side, and a line from the center to the top right angle is "almost" a 306090 triangle with a relationship for the sides. The side of the octagon would be (smaller than): 2*8/SQRT(3).
But, that's not what you wanted. Here's a nontrig approach.
So, think of the octagon as a square with the corners clipped off. The clipped off corners are each 454590 triangles. If a leg is x, then the hypotenuse (side of the octagon) is x*SQRT(2). If the corners weren't clipped off, then the side of the square is made up of three segments and they're in the ratio 1: SQRT(2) : 1 and the side of the octagon is the longer of the three segments. Then, the fraction of the whole diameter of the octagon (in this case, 16) is the length of one of the sides of the octagon is SQRT(2) / [2+SQRT(2)]. Multiply this by 16 and you get the side of the octagon. Phew. USE TRIG!!Last edited by kweaver; 20130503 at 16:27.