In a scalene right triangle where the smallest angle measures 30 degrees, what is a function for the hypotenuse h in terms of the smallest side s?

In a scalene right triangle where the smallest angle measures 30 degrees, the relationships between the angles and sides can be derived from the properties of a 30-60-90 triangle. In such a triangle, the ratios of the lengths of the sides opposite the 30-degree, 60-degree, and right angles are well-defined. Specifically, the side opposite the 30-degree angle is the shortest side, often denoted as "s."

According to the properties of a 30-60-90 triangle, the hypotenuse is always twice the length of the side opposite the 30-degree angle. Therefore, if "s" represents the length of the side opposite the 30-degree angle, the hypotenuse "h" can be expressed as:

[ h = 2s. ]

This relationship arises because the hypotenuse in a 30-60-90 triangle is always the longest side, precisely double that of the shortest side (which corresponds to the side opposite the 30-degree angle).

Thus, the correct function for the hypotenuse in terms of the smallest side is indeed ( h = 2s ).