The word "nonetheless" is an adverb that is used to introduce a contrasting or contradictory statement to what has been previously mentioned. It is often used to show that despite something that has been said or done, the following statement still holds true. Here are a few examples of how to use "nonetheless" in sentences:
"I missed my train and was running late; nonetheless, I managed to arrive on time for the meeting."
"The weather was terrible, with heavy rain and strong winds. Nonetheless, we decided to go ahead with our outdoor picnic."
"She had doubts about her abilities, but nonetheless, she decided to take on the challenge."
"The project faced numerous obstacles and setbacks; nonetheless, we were able to complete it successfully."
"He was exhausted from a long day at work; nonetheless, he mustered the energy to go to the gym."
In each of these examples, "nonetheless" is used to introduce a contrasting or contradictory statement that highlights an unexpected or contrary outcome or situation, despite what may have been expected or previously mentioned.