Дано: tg(α) = 3

sin(α) = tg(α) / √(1 + tg^2(α))
sin(α) = 3 / √(1 + 3^2)
sin(α) = 3 / √10
sin(α) = 3√10 / 10

sin^2(α) = (3√10 / 10)^2
sin^2(α) = (9 * 10) / (10^2)
sin^2(α) = 90/100
sin^2(α) = 0.9

Ответ: sin^2(α) = 0.9