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| Math Central | Quandaries & Queries |
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Question from jacob, a student: hello. i am trying to draw a template for a project. but i don't have a protractor. i'm trying to draw a normal pentagon with 2cm sides. what i'm trying to figure out is the distance in centimeters from point a, to c, in a straight line. this is needed so that i can measure and create the shape without a protractor, and keep the angles and sides correct. if you can help me with the measurement, or help me another way, any help would be greatly appreciated. thank you. |
Hi Jacob,
I can help you get started. Write back if you need more help.
I drew the diagram you described and extended the side ab to a point d.
The angle cbd is an exterior angle of the pentagon. For any convex polygon the sum of the exterior angles is What is the measure of the angle cbd?
Penny
Jacob,
My colleague Chris commented on my response to you. He said
"I saw Penny's answer, but it's a long way from that to what jacob wanted -- he said he doesn't have a protractor, and to get the measure of the diagonal ac from knowing the angle at a vertex requires some facility with geometry. Why not simply tell him to multiply 2cm (which is the side length) by the golden section (1 + sqrt 5)/2 which is approximately 1,618."
Penny
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