An ellipse is a curved shape that resembles a flattened circle, while a triangle is a three-sided polygon with straight sides and angles.
In geometry, an ellipse and a triangle may be related in a problem by intersecting or being tangential to each other, creating various angles and lengths that must be solved for.
The area of an ellipse can be calculated using the formula A = πab, where a and b are the lengths of the semi-major and semi-minor axes. The area of a triangle can be found using the formula A = ½bh, where b is the base length and h is the height.
An inscribed triangle is one that is drawn inside an ellipse, with all three of its vertices touching the ellipse. A circumscribed triangle is one that is drawn outside the ellipse, with all three of its sides touching the ellipse.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem can be used to find missing side lengths or angles in both ellipse and triangle problems.