Verified answer

a)

[tex]sen \alpha = \frac{2}{ \sqrt{13} } . \frac{ \sqrt{13} }{ \sqrt{13} } = \frac{2 \sqrt{13} }{13} \\ \\ cos \alpha = \frac{3}{ \sqrt{13} } . \frac{ \sqrt{13} }{ \sqrt{13} } = \frac{3 \sqrt{13} }{13} \\ \\ tg \alpha = \frac{2}{3} [/tex]

b)

[tex]sen \alpha = \frac{1}{ \sqrt{5} } . \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{ \sqrt{5} }{5} \\ \\ cos \alpha = \frac{2}{ \sqrt{5} } . \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{2 \sqrt{5} }{5} \\ \\ tg \alpha = \frac{1}{2} [/tex]

2)

[tex]tg30 = \frac{h}{8} \\ 0.58 = \frac{h}{8} \\ h = 0.58 \times 8 \\ h = 4.64m [/tex]