Finding Length of Diagonals of Rhombus

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SUMMARY

The discussion focuses on calculating the lengths of the diagonals of a rhombus with sides measuring 100 centimeters and an angle of 70 degrees. Using the Law of Cosines, participants confirm that the opposite angle is also 70 degrees, leading to the remaining angles being 110 degrees each. The calculated lengths of the diagonals are approximately 114.7 centimeters and 163.8 centimeters, validating the approach taken by the participant.

PREREQUISITES
  • Understanding of the properties of a rhombus
  • Familiarity with the Law of Cosines
  • Basic trigonometry concepts
  • Ability to solve for triangle side lengths
NEXT STEPS
  • Study the Law of Cosines in-depth
  • Explore properties of quadrilaterals, specifically rhombuses
  • Learn how to derive diagonal lengths in other polygons
  • Practice solving geometry problems involving angles and side lengths
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Students studying geometry, mathematics educators, and anyone interested in solving problems related to the properties of rhombuses and triangle calculations.

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Homework Statement



A rhombus has sides of length 100 centimeters and the angle at one of the vertices is 70 degrees. Approximate the lengths of the diagonals.

Homework Equations


Law of cosines


The Attempt at a Solution



I just want to make sure I have correct assumptions about a rhombus. If one vertices angle is 70 degrees, that means the opposite is as well. Since all four angles should equal 360 degrees, this means that the other remaining angles at 110 degrees each.

This is basically solving for a side of two triangle, I have two side lengths and an angle. My answers came out to about 114.7 centimeters and 163.8 centimeters.

Thanks Again :)
 
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