A Heron triangle and a Diophantine equation

Given any positive integer n , it is well known that there always exists a triangle with rational sides a , b and c such that the area of the triangle is n . For any pair of primes ( p , q ) such that p ≢ 1 (mod 8) and p 2 + 1 = 2 q , we look into the possibility of the existence of triangles having rational sides with p as the area and p - 1 as tan θ 2 for one of the angles θ . We also discuss the relation of such triangles with the solutions of certain Diophantine equations.