In multi-hop wireless networks, per-hop forwarding strategies that optimize local transmissions can have a subtle impact on network performance. Motivated by a number of scenarios for improving signal strength or mitigating interference, we study a fundamental problem that arises in a wireless ad hoc network with directional transmission (e.g., using directional antennas), where nodes are randomly placed with their transmission footprints (each as a sector) aligned toward the destinations. Only the nodes located in the transmission footprint of a transmitter act as forwarders. Our study addresses connectivity of this setting. We first examine through simulation the percolation probability and the number of cross-area paths available to directional transmission, at different spread angles of transmission footprints. We observe that there is a critical spread angle, above which there is little impact on these properties. Analytically, we derive upper and lower bounds for the critical spread angle. Moreover, we show that with high probability there exist at least Ω(n/ log n) number of disjoint paths across a strip area of n × Θ(n), when the critical spread angle lies above the threshold. Our results provide insights on optimizing directional transmission in wireless ad hoc networks.