Snapped Palm Tree

A palm tree has snapped in a storm. What is the height of the piece that is still standing?
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A palm tree that was 16 metres tall has snapped in a storm, so that the top of the palm tree has landed 8 metres from the base.

What is the height of the piece of the trunk that is still standing (vertically)?

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Snapped Palm Tree
              
Image
Snapped Palm Tree


This problem is adapted from the World Mathematics Championships