Final answer:
The Pythagorean theorem states that in a right-angled triangle, the hypotenuse's length is found by sqrt(a² + b²). This theorem is a reliable principle used to calculate distances in geometry and trigonometry and exemplifies the consistency necessary for theories in physics.
Step-by-step explanation:
The question involves the Pythagorean Theorem, a fundamental principle in trigonometry and geometry. According to Figure 3.4, the Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This relationship is expressed as a² + b² = c². To find the length of the hypotenuse, you can use the formula c = √(a² + b²).
When we apply this theorem consistently, the result should always be the same, provided we carry out the calculations correctly. This demonstrates the reliability of mathematical postulates and their applications. Much like the consistency found in mathematics, theories in physics must be coherent with nature and validated through experiments. They are based on a set of postulates, and when those are accurately selected, predictions can be obtained and confirmed by experimental evidence.
For example, to calculate the hypotenuse's length in a practical scenario, take a right-angled triangle where one side measures 9 blocks and the other side measures 5 blocks. The hypotenuse's length would be √(9 blocks)² + (5 blocks)² = 10.3 blocks, which is more efficient than walking 14 blocks along the two sides separately.