Final answer:
The relationship between angles in a triangle can be determined through the application of the Pythagorean theorem and trigonometry. These mathematical principles serve not just as descriptions but as verified postulates that accurately determine the properties of triangles.
Step-by-step explanation:
The relationship between angles can be determined using mathematical concepts such as the Pythagorean theorem and trigonometry. For instance, if you're working with a right-angled triangle, the Pythagorean theorem would be useful. It describes the relationship between the sides of a right-angled triangle: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is often written as a2 + b2 = c2 where c represents the length of the hypotenuse and a and b the lengths of the other two sides.
Trigonometry is also crucial for determining relationships between angles, especially in non-right angled triangles. It's based on the relationships between the angles and sides of triangles, specifically the ratios of different lengths of sides in right triangles.
These mathematical rules are not merely descriptive but are integral postulates that are proven to hold true across a variety of scenarios, as implied by both the Pythagorean theorem and principles of trigonometry.
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