SOLUTION: Please help me with my project... A regular pentagon is inscribed in a circle of whose radius is 18 cm. Find the perimeter of the pentagon...THANKS...I NEED IT NOW...THANK YOU SO

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Question 846877: Please help me with my project...
A regular pentagon is inscribed in a circle of whose radius is 18 cm. Find the perimeter of the pentagon...THANKS...I NEED IT NOW...THANK YOU SO SO SO SO MUCH
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Please help me with my project...
A regular pentagon is inscribed in a circle of whose radius is 18 cm. Find the perimeter of the pentagon...
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Sketch the figure and draw the 5 triangles formed by the sides and
radii.
The central angle of each triangle is 360/5 = 72 degrees
The base angles are each (180-72)/2 = 108/2 = 54 degrees
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Draw a perpendicular bisector to the base of one of the
triangles; thus forming 2 right triangles.
For one of those two triangles determine the base.
hypotenuse = 18 cm
base angle = 54 degrees
cos(54 deg) = base/18
base = 18*cos(54) = 10.58 cm
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whole side of one side of the pentagon = 2*10.58 = 21.16 cm
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Perimeter of the pentagon = 5*21.16 = 105.8 cm
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Cheers,
Stan H.
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