In triangle ABC, right-angled at C, the value of si$n^2$A + si$n^2$B + co$s^2$C is:

A and $B$ are complementary, so sinB = cosA and si$n^2$A + si$n^2$$B$ = si$n^2$A + co$s^2$$A=1$. The last term is co$s^2$90° = 0, so the total is 1 whatever the side lengths. Treating si$n^2$A + si$n^2$$B$ as two separate 'full' squares suggests 2, reading C as 45° adds a spurious 1/2 to give 3/2, and 0 would need every term to vanish.