Age of fossils is determined by

Radiocarbon dating is a method used to determine the age of organic materials. This method measures the amount of carbon-14 remaining in a sample and compares it to the initial amount of carbon-14. Since the half-life of carbon-14 is approximately 5,700 years, this method can be used to date materials that are up to about 50,000 years old.
Magnetic resonance imaging (MRI) is a medical imaging technique that uses a magnetic field and radio waves to create detailed images of the body. 
Spectroscopy is a method used to analyse the interaction between matter and electromagnetic radiation, such as light. 
Computed tomography (CT) is a medical imaging technique that uses X-rays and computer algorithms to create three-dimensional images of the inside of the body.