Question 451483
Let A be the given (acute) angle.  Then the side adjacent to angle A will have length c*cosA, where c is the length of the hypotenuse.  Then the area of the right triangle is then 

{{{(1/2)c*cosA*c*sin A = (1/2)c^2*sin A*cosA = (c^2*sin(2A))/4}}}