Final answer:
Sketching a triangle with angles totaling more than 180° is not possible due to the Triangle Angle Sum Theorem, thus angles must be adjusted to fit within the necessary constraints of 180° total for a valid triangle in Euclidean geometry.
Step-by-step explanation:
The sketching of a triangle with the given angles and side lengths as mentioned is not possible. In a triangle, the sum of the interior angles must be exactly 180°. However, the question specifies an angle ∠A which is 509°, exceeding this limit significantly. It would be appropriate here to clarify that a valid triangle cannot have an angle of 509°. When such confusion arises, refer to the Triangle Angle Sum Theorem, which states that in Euclidean space, the sum of the angles of a triangle is always 180°.
The other information provided, such as the vector examples and the Pythagorean theorem (a² + b² = c²), are related concepts used in different contexts. For instance, the Pythagorean theorem applies to right-angled triangles and is used to calculate the length of the hypotenuse, or in vector calculations to determine magnitudes.
In summary, the premise of sketching a triangle with the given dimensions is incorrect and it cannot be executed. If the angles were to be adjusted to be within the necessary constraints, the sketch of the triangle could be drawn using conventional geometry tools like a ruler (for side length) and a protractor (for angle measurements).