Finding distance between two adjacent objects

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  • Thread starter Thread starter chr1is
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SUMMARY

The distance between two adjacent holes drilled in a metal plate arranged in a circle with a radius of 16.40 cm can be calculated using the Law of Cosines or the Law of Sines. With 12 equally spaced holes, the angle subtended by each pair of adjacent holes is 30 degrees. Applying the Law of Cosines, where the two equal sides are the radius (16.40 cm) and the angle is 30 degrees, allows for the calculation of the distance between the holes. The Law of Sines can also be utilized for a simpler computation.

PREREQUISITES
  • Understanding of basic trigonometry concepts, specifically the Law of Cosines and Law of Sines.
  • Familiarity with geometric properties of circles.
  • Ability to perform calculations involving angles and distances.
  • Knowledge of isosceles triangles and their properties.
NEXT STEPS
  • Study the Law of Cosines in-depth for various applications in geometry.
  • Explore the Law of Sines and its use in solving triangles.
  • Learn about geometric constructions involving circles and angles.
  • Practice calculating distances in circular arrangements with different radii and hole counts.
USEFUL FOR

Mathematicians, engineering students, and anyone involved in design or manufacturing processes that require precise measurements in circular layouts.

chr1is
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I have a question:

Holes are to be drilled in a metal plate at 12 equally spaced locations around a circle with a radius of 16.40 cm. Find the distance between two adjacent holes.

How do I draw the figure? And would I have to multiply 16.40 by 2 to get the distance?
 
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One way would be to use the Law of Cosines...form an isosceles triangle using the center of the circle and two adjacent holes...you know the two equal sides of the triangle are the radius of the circle, and you know the angle subtending these sides, so you can find the third side using the Law of Cosines. You could also use the Law of Sines here as well, which would likely be computationally simpler.
 

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