Determine distance of asteroid based on two observations from different locations
Draw a diagram.
You get a quadrilateral EACB.  You should be able to determine the four angles in the quadrilateral.
Draw the diagonal EC, which is the length to be determined.
You know that ACE + BCE = ACB  (the known angle at the asteroid)
And you can use the law of sines twice, once in each of the triangles EAC and EBC
These should give you three equations, with three unknowns:  length EC,  and angles ACE and BCE.  Given three equations and three unknowns, a solution should be possible. You should find the distance is a little more than the Earth-moon distance.
Note that angles at the centre made by the diagonal: AEC and BEC are not 46° 27' and  22° 34', but the sum of those angles is the sum of 46° 27' + 22° 34'