Final answer:
The Pythagorean theorem calculates the hypotenuse in a right triangle, which is √(leg1² + leg2²). It provides the shortest straight-line path between two points, which in the provided example is √(9² + 5²) = 10.3 blocks.
Step-by-step explanation:
The question refers to using the Pythagorean theorem to calculate the hypotenuse of a right triangle given its legs. When you have a right triangle with legs of lengths A and B, the hypotenuse, C, is determined by the relationship C = √(A²+B²).
If we have a right triangle with legs of 9 blocks and 5 blocks, as per the provided information, we can calculate the hypotenuse as √(9 blocks)² + (5 blocks)² = 10.3 blocks. The length of the hypotenuse will always be the direct straight-line distance between the two points forming the right angle and is thus shorter than walking along the two legs of the triangle.
It's important to note that the straight-line path is more efficient.
Therefore, when selecting a limit or establishing a boundary for the hypotenuse, one should use the actual hypotenuse calculation √(A²+B²) rather than a simple sum or an arbitrary value such as 6.97 unless there are specific reasons for doing so. The calculation of direction direction = tan⁻¹(B/A) = 29.1° is also based on the lengths of the legs of the triangle and is consistent with the example provided.