Explicación paso a paso:
■ Solución:
[tex] \frac{2n - 5}{n + 5} = \frac{3}{4} \\ \\ 4(2n - 5) = 3(n + 5) \\ \\ 8n - 20 = 3n + 15 \\ 8n - 3n = 15 + 20 \\ 5n = 35 \\ n = 7[/tex]
Lado opuesto a 37° mide: (2n - 5) = 2(7) - 5 = 14 - 5 = 9
Lado adyacente a 37° mide: n + 5 = 7 + 5 = 12
La hipotenusa mide: 15
[tex] {h}^{2} = {9}^{2} + {12}^{2} \\ {h}^{2} = 81 + 144 \\ {h}^{2} = 225 \\ h = \sqrt{225} \\ h= \sqrt{ {15}^{2} } \\ h \: = 15[/tex]
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Explicación paso a paso:
■ Solución:
[tex] \frac{2n - 5}{n + 5} = \frac{3}{4} \\ \\ 4(2n - 5) = 3(n + 5) \\ \\ 8n - 20 = 3n + 15 \\ 8n - 3n = 15 + 20 \\ 5n = 35 \\ n = 7[/tex]
Lado opuesto a 37° mide: (2n - 5) = 2(7) - 5 = 14 - 5 = 9
Lado adyacente a 37° mide: n + 5 = 7 + 5 = 12
La hipotenusa mide: 15
[tex] {h}^{2} = {9}^{2} + {12}^{2} \\ {h}^{2} = 81 + 144 \\ {h}^{2} = 225 \\ h = \sqrt{225} \\ h= \sqrt{ {15}^{2} } \\ h \: = 15[/tex]