Answer
Please see the work below.
Work Step by Step
We know that according to law of conservation of energy
$(\frac{1}{2})mv^2=mg(L-Lcos(\theta))$
This simplifies to:
$(\frac{1}{2})v^2=gL(1-cos(\theta))$
$L=\frac{v^2}{2g(1-cos(\theta))}$
We plug in the known values to obtain:
$L=\frac{(0.55)^2}{(2)(9.8)(1-cos(8.0))}$
$L=1.6m$
