Question

Determine o valor de m, n, h e x no triângulo retângulo.​

Answer 1

Resposta:

m = 45

n = 15

$h = 15 \sqrt{3}$

x = 60

Explicação passo-a-passo:

$\sin(60) = \frac{h}{30} \\ \\ \frac{ \sqrt{3} }{2} = \frac{h}{30} \\ \\ 30 \sqrt{3} = 2h \\ h = \frac{30 \sqrt{3} }{2} \\ \\ h = 15 \sqrt{3}$

${30}^{2} = {h}^{2} + {n}^{2} \\ 900 = {(15 \sqrt{3} )}^{2} + {n}^{2} \\ 900 = 225 \times 3 + {n}^{2} \\ 900 = 675 + {n}^{2} \\ {n}^{2} = 900 - 675 \\ {n}^{2} = 225 \\ n = \sqrt{225} \\ n = 15$

${h}^{2} = m \times n \\ {(15 \sqrt{3} )}^{2} = 15m \\ 675 = 15m \\ m = \frac{675}{15} \\ \\ m = 45$

x = m + n

x = 45 + 15

x = 60