Draw the following regular polygons inscribed in a circle:
1 answer:
Answer:
- first attachment has pentagon and decagon
- second attachment has hexagon and dodecagon
- computation info explained below
Step-by-step explanation:
<u><em>1, 2. Central Angle, Interior Angle</em></u>
See the 3rd attachment for the values. (Angles in degrees.)
The central angle is 360°/n, where n is the number of vertices. For example, the central angle in a pentagon is 360°/5 = 72°.
The interior angle is the supplement of the central angle. For a pentagon, that is 180° -72° = 108°.
These formulas were implemented in the spreadsheet shown in the third attachment.
<u><em>3. Angles vs. Number of Sides</em></u>
The size of the central angle is inversely proportional to the number of sides. In degrees, the constant of proportionality is 360°.
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<em>Comment on the drawings</em>
The drawings are made by a computer algebra program that is capable of computing the vertex locations around a unit circle based on the number of vertices. The only "work" required was to specify the number of vertices the polygon was to have. The rest was automatic.
The above calculations describe how the angles are computed. Converting those to Cartesian coordinates for the graphics plotter involves additional computation and trigonometry that are beyond the required scope of this answer.
These figures can be "constructed" using a compass and straightedge. No knowledge of angle measures is required for following the recipes to do that.
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Answer: 2.12 ×
The coefficient (in green) will be 2.12
Step-by-step explanation:
Scientific notation is written by multiplying the number by a power of 10. This number is a number between 1 and 10.
Since this is a smaller number, we will be multiplying it by a power of 10 to a negative number.
To get this value to a number between 1 and 10, we must multiply it by 10 3 times (also shown as 10³) which gives us 2.12.
To get back to the original value, we multiply this by . This gives us our answer.