You can tell a surprising amount from teeth. Bones and teeth the most highly mineralised in the body. They are connective tissues, which are tissues in which the living cells are suspended in a matrix of protein fibres and impregnated with inorganic minerals. In bone the living cells are osteoclasts and the inorganic mineral is calcium. The purpose of this is to make the tissue hard and durable, which is why bones, and teeth, remain long after a body has decomposed.
The dentition is informative about the diet and therefore a diagnostic aid to identification.
Broadly speaking, the animals can be divided into herbivores, carnivores and omnivores. This classification is reflected in the type and number of teeth.
Herbivores have a teeth that are adapted for cutting plant material and then chewing it for long periods to break down the cell walls. They have sharp incisors which act like scissors, and then a number of broad flat molars that grind in a side to side or round and round motion (chewing the cud).
Carnivores have large, sharp canines, for puncturing and tearing meat, and their jaw opens up and down to provide great force, but does not go side to side to chew.
Omnivores have small incisors, small canines and some molars, which is an adaptation to their varied diet.
We can deduce by the number of molars that this animal was a herbivore and most likely a sheep. (Also because it was found in the Welsh hills!)