  The $\vec{p}p \rightarrow pK^{+}\Lambda$ reaction has been measured with the
COSY-TOF detector at a beam momentum of $2.7\,\mathrm{GeV}/c$. The polarized
proton beam enables the measurement of the beam analyzing power by the
asymmetry of the produced kaon ($A_N^{K}$). This observable allows the
$p\Lambda$ spin triplet scattering length to be extracted for the first time
model independently from the final-state interaction in the reaction. The
obtained value is $a_{t} = (-2.55 ^{+0.72}_{-1.39} {}_{\textrm{stat.}} \pm
0.6_{\textrm{syst.}} \pm 0.3_{\textrm{theo.}})\mathrm{fm}$. This value is
compatible with theoretical predictions and results from model-dependent
analyses.
