How many distinct triangles ABC are there, up to similarity, such that the magnitudes of angles A, B and C in degrees are positive integers and satisfy A B+ A B k C=1

Step-by-step solution

aligned & A B+ A B k C=1 & A B+ A B+ A B k C- A B=1 & A B( k C-1)=1- (A-B) aligned So ( k C-1)=0 and (A-B)=1 kC =90^ and A = B Number of factors of 90^ 90=2 3^2 5 Number of factors =2 3 2=12 for 6 factor A, B are integers