What is "given right triangle def?

A "given right triangle DEF" means we're dealing with a triangle that has the following characteristics:

• Right Triangle: One of the angles in the triangle is a right angle (90 degrees). This is usually indicated by a small square in the corner of the angle.
• Vertices D, E, F: The vertices (corners) of the triangle are labeled D, E, and F. Conventionally, the right angle is often at vertex E, so angle E = 90°. But this isn't always the case; it could be at D or F.
• Sides DE, EF, DF: The sides of the triangle are opposite the vertices with the same letters. The side opposite the right angle (the longest side) is called the hypotenuse. In a right-angled triangle, the Pythagorean theorem applies (a² + b² = c², where 'c' is the hypotenuse).

Without more information about the triangle DEF (like the lengths of its sides or the measures of its angles), we can't say more. The "given" part implies that some additional information will be provided to allow for calculations or problem-solving. This information could include:

• Side lengths: The lengths of sides DE, EF, and DF.
• Angle measures: The measures of angles D and F (besides the known 90-degree angle).
• Relationships between sides: Information about ratios of side lengths (e.g., "DE is twice the length of EF").

Once that additional information is given, we can use trigonometry, geometry, or the Pythagorean theorem to solve for unknowns.