Resposta:
m = 45
n = 15
[tex]h = 15 \sqrt{3} [/tex]
x = 60
Explicação passo-a-passo:
[tex] \sin(60) = \frac{h}{30} \\ \\ \frac{ \sqrt{3} }{2} = \frac{h}{30} \\ \\ 30 \sqrt{3} = 2h \\ h = \frac{30 \sqrt{3} }{2} \\ \\ h = 15 \sqrt{3} [/tex]
[tex] {30}^{2} = {h}^{2} + {n}^{2} \\ 900 = {(15 \sqrt{3} )}^{2} + {n}^{2} \\ 900 = 225 \times 3 + {n}^{2} \\ 900 = 675 + {n}^{2} \\ {n}^{2} = 900 - 675 \\ {n}^{2} = 225 \\ n = \sqrt{225} \\ n = 15[/tex]
[tex] {h}^{2} = m \times n \\ {(15 \sqrt{3} )}^{2} = 15m \\ 675 = 15m \\ m = \frac{675}{15} \\ \\ m = 45[/tex]
x = m + n
x = 45 + 15
x = 60
