Question 198770
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If the pentagon is inscribed in a circle, then a side of the pentagon is a chord of the circle.  Since it is a regular pentagon, the angle subtended by such a chord is one-fifth of the circle, or *[tex \Large \frac{2\pi}{5}] radians.


Knowing the radius and the subtended angle, you can calculate the chord length using:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C = 2r\sin\left(\frac{c}{2}\right)\ =\ 2\cdot4\cdot\sin\left(\frac{\pi}{5}\right)\]


Where *[tex \Large r] is the radius of the circle and *[tex \Large c] is the subtended angle.


All you need to do now is a little calculator work.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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