Question 1092244
(1)  {{{ y^2 + z^2 = (8+19)^2 }}}
(2)  {{{ x^2 + 8^2 = z^2 }}}
(3) {{{ x^2 + 19^2 = y^2 }}}

Solving (I used substitution for {{{ z^2}}} in (2) and {{{ y^2 }}} in (3) into (1)):
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Ans:
{{{ highlight(x=sqrt(152)) }}}
{{{ highlight(y=sqrt(513)) }}}
{{{ highlight(z=sqrt(216)) }}}
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Check:
 {{{y^2 + z^2 = 513+216 = 729 = 27^2 = (8+19)^2 }}} (ok)
 {{{ x^2 + 8^2 = 152+64 = 216 = z^2 }}}  (ok)
 {{{ x^2 + 19^2 = 152+361 = 513 = y^2 }}}  (ok)