Final answer:
To determine the black cow's genotype, a farmer would mate the black-haired cow with a homozygous black-haired cow.
Step-by-step explanation:
In cattle, black hair color is dominant to red hair color. To determine the black cow's genotype, a farmer would mate the black-haired cow with a homozygous black-haired cow. This is because a homozygous black-haired cow will always have two copies of the dominant black allele (BB), which will allow the farmer to determine if the black cow is homozygous (BB) or heterozygous (Bb) for black hair color.