Explicação passo-a-passo:

[tex]a) \sin(45) = \frac{y}{20 \sqrt{2} } \\ \\ \frac{ \sqrt{2} }{2} = \frac{y}{20 \sqrt{2} } \\ \\ 20 \sqrt{2} \times \sqrt{2} = 2y \\ 2y = 20 \times 2 \\ 2y = 40 \\ y = \frac{40}{2} \\ \\ y = 20 \\ \\ \cos(45) = \frac{x}{20 \sqrt{2} } \\ \\ \frac{ \sqrt{2} }{2} = \frac{x}{20 \sqrt{2} } \\ \\ 20 \sqrt{2} \times \sqrt{2} = 2x \\ 20 \times 2 = 2x \\ 2x = 40 \\ x = \frac{40}{2} \\ \\ x = 20[/tex]

[tex]b) \tan(30) = \frac{x}{9 \sqrt{3} } \\ \\ \frac{ \sqrt{3} }{3} = \frac{x}{9 \sqrt{3} } \\ \\ 9 \sqrt{3} \times \sqrt{3} = 3x \\ 9 \times 3 = 3x \\ 3x = 27 \\ x = \frac{27}{3} \\ \\ x = 9 \\ \\ \sin(30) = \frac{x}{y} \\ \\ \frac{1}{2} = \frac{9}{y} \\ y = 2 \times 9 \\ y = 18[/tex]