Answer :
In the given right angled triangle,
AC=b=290 cm.
Using trigonometric property in the given triangle,
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan 30\degree=\frac{a}{b} \\ a=b\tan 30\degree \\ a=290\times\frac{1}{\sqrt[]{3}} \\ a=167\text{ cm} \end{gathered}[/tex]Therefore, the value of a is 167 cm.