How is ageism related to sociology?

Actually, it might be closer to anthropology-- which is an academic field aligned with sociology. Sociologists and anthropologists study a society's attitudes about aging: the effects of age discrimination, and the culture's myths, stereotypes, and social rituals about the elderly; how older people are treated, etc. Both of these disciplines also examine what roles in a society older people play, and what roles they are excluded from. For example, some societies revere and take care of their aged members, treating them with the utmost respect, while others seem to regard the elderly as a bother and either abandon them or put them away in institutions. In some cultures, being old is considered a sign of wisdom, whereas in other cultures, older people are assumed to have declining mental abilities.