Resposta :
Clara,
Sendo o angulo (90 - x), x pertence ao primeiro quadrante
Então:
sen(90 - x) = cos x
cos x = 2/3
sen^2 x + cos^2 x = 1
sen^2 x + (2/3)^2 = 1
sen^2 x + 4/9 = 1
sen^2 x = 1 - 4/9 = 5/9
sen x = 1/3(raiz de 5)
tag x = sen x / cos x
= [1/3(raiz de 5)] / (2/3) = 3(raiz de 5) / 3.2
tag x = (raiz de 5) / 2
[sen (90-x)]² + (sen x)² = 1
(2/3)² + (sen x)² = 1
4/9 + (sen x)² = 1
(sen x)² = 1 - 4/9
(sen x)² = 5/9
sen x = \/(5/9)
sen x = \/5/\/9
sen x = \/5/3
tg x = sen x / cos x
tg x = \/5/3 / 2/3
tg x = \/5/2