Resposta:

A) sin(30) = 3/x

1/2 = 3/x

x = 2 . 3

x = 6

[tex] \cos(30) = \frac{y}{6} \\ \frac{ \sqrt{3} }{2} = \frac{y}{6} \\ 2y = 6 \sqrt{3} \\ y = \frac{6 \sqrt{3} }{2} \\ y = 3 \sqrt{3} [/tex]

B)

[tex] \sin(60) = \frac{y}{ \sqrt{5} } \\ \frac{ \sqrt{3} }{2} = \frac{y}{ \sqrt{5} } \\ 2y = \sqrt{3} \times \sqrt{5} \\ 2y = \sqrt{15} \\ y = \frac{ \sqrt{15} }{2} [/tex]

[tex] \cos(60) = \frac{x}{ \sqrt{5} } \\ \frac{1}{2} = \frac{x}{ \sqrt{5} } \\ 2x = \sqrt{5} \\ x = \frac{ \sqrt{5} }{2} [/tex]

C)

[tex] \cos(45) = \frac{10}{y} \\ \frac{ \sqrt{2} }{2} = \frac{10}{y} \\ \sqrt{2} y = 20 \\ y = \frac{20}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ y = \frac{20 \sqrt{2} }{2} \\ y = 10 \sqrt{2} [/tex]

[tex] \sin(45) = \frac{x}{10 \sqrt{2} } \\ \frac{ \sqrt{2} }{2} = \frac{x}{10 \sqrt{2} } \\ 2x = 10 \sqrt{2} \times \sqrt{2} \\ 2x = 10 \times 2 \\ x = \frac{10 \times 2}{2} \\ x = 10[/tex]