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Math Help - euclidean construction of the regular pentagon

  1. #1
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    euclidean construction of the regular pentagon

    using trigonometry in right triangle ABF in unit circle O with diameter AB of length 2, show that AF=t and cos(theta) = t/2, so that theta = 36, measure of angleFOB=72, and the construction yields a regular pentagon.

    I can not for the life of me figure this out. The construction steps are 1. starting with diameter AB, construct CO perpendicular to AB. 2. Construct the midpoint D of AO. 3. construct point E on AB so that DE = DC. 4. Construct point F on the circle so that AF= AE. 5. Draw segment BF. This is a side of the regular pentagon.
    I am confused.
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  2. #2
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    Quote Originally Posted by janae77 View Post
    using trigonometry in right triangle ABF in unit circle O with diameter AB of length 2, show that AF=t and cos(theta) = t/2, so that theta = 36, measure of angleFOB=72, and the construction yields a regular pentagon.

    I can not for the life of me figure this out. The construction steps are 1. starting with diameter AB, construct CO perpendicular to AB. 2. Construct the midpoint D of AO. 3. construct point E on AB so that DE = DC. 4. Construct point F on the circle so that AF= AE. 5. Draw segment BF. This is a side of the regular pentagon.
    I am confused.
    Have a look here: Pentagon - Wikipedia, the free encyclopedia

    Scroll down a little bit until you came to the item "Construction"
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