This is the only solution, except that you may reverse the arrangement from left to right.
For more about this puzzle, see Martin Gardner's Penrose
Tiles to Trapdoor Ciphers (New York, W. H. Freeman, 1989;
Washington, Mathematical Association of America, 1996;
Cambridge, Cambridge University Press, 1997), Chapter 9;
and Brian Chen, Yunhao Fu, Andy Liu, George Sicherman, Herbert Taylor,
and Po-Sheng Wu,
Triangles of Absolute Differences,
Gathering for Gardner 9 (Atlanta, 2010).