Note: Assumed person graphed the triangle in the ellipse.

Algebratic Solution:

We start by making one vertex not the point given . The other vertices are respectively. We note that the disyance between all the points must be the same. Distance formula!

. Squaring both sides,

which implies that .

We can substitue this back into the ellispe equation:

. Using the qaudratic formula, we obtain

. Then

which implies that

, so .

. The distance formula result we want is the side leangth, so

.

Thus our answer is .

Trigonometric Solution:

We note that the slope of the line which is the side of the tringle is the tangent of 60 (rise over run=y over x). The line has points

, so the slope is . Since it equals the tangent of 60, we have:

. Cross multiplying,

implies .

We plug this back in the ellispe equation:

, so we have

.

The only plausible solution is .

This gives a solution for y: .

Computing the distance between and using the distance formula, we have

.

Thus our answer is .