That depends on how the vertices of the triangle are labeled.

If the triangle is labeled like this:

 then BC is also 10 feet 

So we use the Pythagorean theorm:

AC² = AB² + BC²
AC² = 10² + 10²
AC² = 100 + 100
AC² = 200
 AC = Ö200
 AC = Ö100·2

 AC = 10Ö2

But if the triangle is labeled like this:

 then AC is also 10 feet 

Then the answer is 10 feet and you don't need the Pythagorean theorm,
only the knowledge that isosceles triangles have two sides of equal
length. 

Edwin