You should work out if you have the pre- or post-TS60000 body. The hood/bonnet, like almost every other panel on the car, changed at that point. Although the factory made the switch in late 59, many cars were sold and titled as being later years, so your '60' may have been made before the change.
You can add spacers under the hinges to make the early hood fit the later cars, but it would better to get the right hood. Practically any TR3 fan will spot the difference, even if they don't say anything.