1. The problem involves understanding the properties of a right triangle with a hypotenuse of length $\sqrt{3}$.\n\n2. In a right triangle, the hypotenuse is the longest side, opposite the right angle. The Pythagorean theorem states that for sides $a$, $b$, and hypotenuse $c$, we have $$a^2 + b^2 = c^2.$$\n\n3. Given the hypotenuse $c = \sqrt{3}$, if we know one leg, we can find the other using $$b = \sqrt{c^2 - a^2}.$$\n\n4. For example, if one leg is $1$, then the other leg is $$b = \sqrt{(\sqrt{3})^2 - 1^2} = \sqrt{3 - 1} = \sqrt{2}.$$\n\n5. This triangle could represent a 30-60-90 triangle where the sides are in ratio $1 : \sqrt{3} : 2$, but here the hypotenuse is $\sqrt{3}$, so the sides scale accordingly.\n\n6. Understanding these relationships helps in solving problems involving right triangles and trigonometric ratios.