Final answer:
The hypotenuse is the longest side of a right triangle, opposite the right angle, and the adjacent side forms an angle with the hypotenuse. The hypotenuse length can be calculated using the Pythagorean theorem. The adjacent side's length is used when finding the cosine of an angle in a right triangle.
Step-by-step explanation:
The hypotenuse of a right triangle is defined as the side opposite the right angle, and it is the longest side in the triangle. According to the Pythagorean theorem, if a right triangle has legs of length a and b, with the hypotenuse having length c, the relationship between these sides is a² + b² = c². This theorem can also be expressed as c = √(a² + b²), allowing us to calculate the hypotenuse length when the lengths of the other two sides are known.
The adjacent side of a right triangle refers to the side that, together with the hypotenuse, forms the angle in question (other than the right angle). For example, in a trigonometric context like when calculating the cosine of an angle, the adjacent side is featured in the ratio alongside the hypotenuse (cos A = Ax/A, where Ax represents the length of the adjacent side and A represents the length of the hypotenuse).