# 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.

×