A titled ellipse inscribed in a triangle

Geometry Level 5

A triangle has its vertices at \( A (0,20) \), \( B (-10,0) \) and \( C (20,0) \), as shown in the figure above. We wish to fit an ellipse in the triangle with two conditions:

  • The ratio of major axis to minor axis is 2.
  • The angle that the major axis makes with the horizontal is \( 30^{\circ} \).

Find the length of the major axis of this ellipse. Round your answer to the nearest hundredth.

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