Question

Me podrían ayudar en esta pregunta porfavor

Answer 1

Respuesta:

                    $1$

Explicación paso a paso:

   $a = 8u ;b = 15u ; c = 10u.$

Buscamos los ángula $\alpha$  Y  $\beta$   con la fórmula:

$Cos (\alpha )= \frac{a^{2}+c^{2} -b^{2} }{2ac} = \frac{(8)^{2} +(10)^{2}-(15)^{2} }{2(8)(10)} =\frac{64+100-225}{160} = \frac{-61}{160} = - 0.38125$

$Cos (\alpha ) = -0.38125$

$\alpha =arc Cos (-0.38125) = 112.41$

$\alpha =112.41$

$Cos (\beta )=\frac{b^{2}+c^{2} -a^{2} }{2bc} =\frac{(15)^{2} +(10)^{2} -(8)^{2} }{2(15)(10)} =\frac{225+100-64}{300} = \frac{261}{300} =0.87$

$Cos (\beta ) =0.87$

$\beta =arcCos (0.87)$

$\beta =29.54$

$\frac{\sqrt{160} }{\sqrt{143} *Csc(\frac{\alpha +\beta }{2} )} =\frac{\sqrt{160} }{\sqrt{143} *Csc(\frac{112.41+29.54}{2}) } =\frac{\sqrt{160} }{\sqrt{143} *Csc(70.975)}=\frac{\sqrt{160} }{\sqrt{143}* (1.0578) }$

                         $= \frac{12.6491}{(11.9583)*(1.0578)} = \frac{12.6491}{12.6495} = 0.9999 = 1$    

Respuesta :   1