In triangle PQR, right-angled at Q, PQ = 5 cm and QR = 12 cm. The value of sinP + cosR is:

The hypotenuse is PR = √(25 + 144) = 13 cm. At P the opposite side is QR = 12, so sinP = 12/13; at R the adjacent side is QR = 12, so cosR = 12/13. The sum is 24/13. The two ratios agree because P and R are complementary — spotting that and then reporting a single ratio gives 12/13. Using sinR = 5/13 by mistake gives 17/13, and pairing the side 5 with both angles gives 10/13.