Question

Trigonometría
Indica el valor:
​

Answer 1

Respuesta:

$\sqrt{19}$

Explicación paso a paso:

*se sabe:

→ a²-b²=(a-b)(a+b)

→ S/180 = C/200

simplificando

S/9 = C/10 =k

∴ S=9k

  C=10k

*resolviendo:

$M=\sqrt{4+\frac{5(C-S)^{2} }{C^{2}-S^{2}}}  +   \sqrt{6-\frac{14(C^{2}-S^{2})}{(C+S)^{2} } }\\M=\sqrt{4+\frac{5(C-S)^{2} }{(C-S)(C+S)}}   +   \sqrt{6-\frac{14(C-S)(C+S)}{(C+S)^{2} } }\\M=\sqrt{4+\frac{5(C-S)}{(C+S)}}  +  \sqrt{6-\frac{14(C-S)}{(C+S)}}\\M=\sqrt{4+\frac{5(10k-9k)}{(10k+9k)}}  +  \sqrt{6-\frac{14(10k-9k)}{(10k+9k)}}\\M=\sqrt{4+\frac{5k}{19k}} + \sqrt{6-\frac{14k}{19k}}\\M=\sqrt{4+\frac{5}{19}}  +  \sqrt{6-\frac{14}{19}}\\M=\sqrt{\frac{81}{19}}  +  \sqrt{\frac{100}{19}}$

$M=\frac{9}{\sqrt{19} } + \frac{10}{\sqrt{19} } \\M=\frac{19}{\sqrt{19} } \\M=(\frac{19}{\sqrt{19} })(\frac{\sqrt{19} }{\sqrt{19} } )\\\\M=\frac{19\sqrt{19} }{19} \\M=\sqrt{19}$