Answer
$7.17 \ m$
Work Step by Step
Using the definition of tangent of the angle A, we have
$$
\tan A=\tan 29.7=\frac{length \ of \ side\ opposite\ angle\ A}{length \ of \ side\ adjacent\ angle\ A}=\frac{4.09}{b}
.$$
That is,
$$
b= \frac{4.09}{\tan 29.7}=7.17 \ m
.$$
