  It is well-known that there exists a triangle-free planar graph of $n$
verticess such that the largest induced forest has size at most $\frac{5n}{8}$.
Salavatipour proved that there is a forest of size at least $\frac{5n}{9.41}$
in any triangle-free planar graph of $n$ vertices. Dross, Montassier and Pinlou
improved Salavatipour's bound to $\frac{5n}{9.17}$. In this work, we further
improve the bound to $\frac{5n}{9}$. Our technique is inspired by the recent
ideas from Lukot'ka, Maz{\'a}k and Zhu.
