Help triangle within a circle find side of triangle

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SUMMARY

The problem involves calculating the length of a side of an equilateral triangle inscribed in a circle with a radius of 2.9 meters. By drawing lines from each vertex of the triangle to the center of the circle, the triangle is divided into three isosceles triangles. Using trigonometric principles, specifically the properties of isosceles triangles and the known radius, one can derive the length of the triangle's side. The solution utilizes fundamental trigonometric functions to achieve the final measurement.

PREREQUISITES
  • Understanding of equilateral triangle properties
  • Knowledge of isosceles triangle characteristics
  • Familiarity with basic trigonometry
  • Ability to apply the Law of Cosines
NEXT STEPS
  • Study the Law of Cosines for triangle side calculations
  • Explore trigonometric functions and their applications in geometry
  • Learn about inscribed angles and their properties
  • Investigate the relationship between radius and side lengths in polygons
USEFUL FOR

Students of geometry, mathematics educators, and anyone interested in solving geometric problems involving circles and triangles.

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The corners of an equilateral triangle lie on a circle of radius 2.9 m. Find the length of a side of the triangle.

find meters
 
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One way is to draw a line from each vertex of the triangle to the centre of the circle, splitting the equilateral triangle into 3 isosceles. If you consider one of these triangles, you can fairly easily work out all the internal angles, and you know the length of two of the sides of the isosceles triangle (the radius of the circle). From here you just use trigonometry to find the length of the third side, which is the length of the side of the triangle.
 

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