Remember that
A right triangle must satisfy the Pythagorean Theorem
so
c^2=a^2+b^2
Find the possible combinations
For c=43 and a=12 , b=35
43^2=12^2+35^2
1,849=144+1,225 -------> is not true
For c=43 and a=35, b=37
43^2=35^2+37^2
1,849=1,225+1,369 -----> is not true
For c=37, a=12, b=35
37^2=12^2+35^2
1,369=144+1,225
1,369=1,369 ------> is true
that means
Is a right triangle
the solution is
37,12,35
see the attached figure