Upon completion, Fort Washington controlled the high ground overlooking the Hudson River, thus protecting the American positions from warships. Between the elevation and defenses of Fort Washington and Fort Lee, British ships could not mount an adequate attack against the forts. As a result, the forts were considered critical to the American positions along the Hudson River even though all exterior defenses were not fully completed.
http://totallyhistory.com/battle-of-fort-washington/
˄. Fought on November 16, 1776 on Manhattan, the Battle of Fort Washington underscored General Washington’s disastrous New York Campaign. The battle ended in a resounding British victory with the fort surrendering 3,000 Continental troops and Washington abandoning his defense of New York City.
http://www.campaign1776.org/battlefields/fort-washington/
Three days after the surrender of Fort Washington, American forces abandoned Fort Lee. The remaining American forces under Washington’s command fled across New Jersey and into Pennsylvania.
http://totallyhistory.com/battle-of-fort-washington/
Main article: Battle of Fort Washington. Fort Washington was held by American forces under the command of Colonel Robert Magaw, who refused to surrender the fort to the British. He informed the British that he would fight to the last extremity.
https://en.wikipedia.org/wiki/Fort_Washington_(Manhattan)
Just one in a string of defeats, the battle ended in a resounding British victory with the fort surrendering 3,000 Continental troops and Washington abandoning his defense of New York City.
http://www.campaign1776.org/battlefields/fort-washington/
When the British emissary, Captain Hohenstein, demanded the fort’s surrender, a messenger arrived from Washington. Washington, observing the battle from Fort Lee, sent the messenger to Magaw requesting the fort be held until night with the hopes the remaining forces could be evacuated under cover of darkness.
http://totallyhistory.com/battle-of-fort-washington/
Howe, ignoring Washington in retreat, wheeled his force around and bore down on Fort Washington overlooking the Hudson. The last American stronghold on Manhattan was completely alone as General Washington was now stuck on the opposite side of the Hudson unable to help.
http://www.campaign1776.org/battlefields/fort-washington/
Howe, moving north on the New York mainland, met Washington at the battle of White Plains on the 28th of October, where the Americans suffered yet another defeat, resulting in a retreat further to the north, and away from Fort Washington, which was now left stranded on Manhattan.
http://www.campaign1776.org/battlefields/fort-washington/
At this battle was Margaret Corbin of Virginia, who is recognized as the first female soldier to fight in the American Army. Married to John Corbin of the First Company of the Pennsylvania Artillery, Margaret cleaned, loaded and fired her husband’s cannon when he was killed during the assault on Fort Washington.
https://en.wikipedia.org/wiki/Fort_Washington_(Manhattan)
The modern day location of Fort Washington is marked by Bennett Park on Fort Washington Ave. between West 183rd and West 185th Sts. in the Hudson Heights neighborhood of the Washington Heights section of New York City. The locations of the fort's walls are marked in the park by stones, along with an inscription.
https://en.wikipedia.org/wiki/Fort_Washington_(Manhattan)
where was fort washington battle
The Battle of Fort Washington was in New York. A  fort Washington battle was New York.