(Originais Teachy 2024) - Question Medium of Mathematics

In a geometry problem, a right triangle has one of the acute angles measuring 30 degrees and the hypotenuse has a length of 2. By defining the side opposite this angle as 'a' and the adjacent side as 'b', we know that the ratio between 'a' and 'b' will be the tangent of 30 degrees, which is equal to 1/√3. To express the length of the adjacent side in terms of the opposite side, we need to rationalize the denominator of the tangent ratio of 30 degrees. (1) Rationalize the denominator of the tangent ratio of 30 degrees and express 'b' in terms of 'a'. (2) What is the exact value of 'b' in this triangle?