Final answer:
In a right triangle, the longest side opposite the right angle is called the hypotenuse. Sides adjacent to the reference angle are called adjacent sides, and the side opposite the reference angle is the opposite side. The Pythagorean theorem allows calculation of the hypotenuse length given the lengths of the other two sides.
Step-by-step explanation:
In mathematics, specifically in trigonometry, we describe the sides of a right-angled triangle relative to one of the angles in terms of hypotenuse, adjacent, and opposite. The hypotenuse is the longest side of a right triangle and is always opposite the right angle. The side of the triangle that is "next to" or adjacent to the reference angle is known as the adjacent side. Conversely, the side opposite the reference angle is the opposite side.
Using the Pythagorean theorem, which states that in a right 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), given by the equation a² + b² = c², we can find the length of the hypotenuse. For example, if a right triangle has legs of 9 and 5 units (possibly representing city blocks), the length of the hypotenuse can be calculated as √(9² + 5²) = √(81 + 25) = √106 ≈ 10.3 units. This use of the Pythagorean theorem shows us that moving diagonally, or in a straight line, is more efficient than moving along the two separate sides.