Length of Sides in an Isosceles Triangle

Triangle DEF is isosceles with sides DE = DF and base EF. The angle at vertex D is 80 degrees. If the length of base EF is 10 units, what is the length of the equal sides DE and DF?

Use the Law of Cosines, which states that for any triangle with sides $a$, $b$, $c$ and corresponding angles $A$, $B$, $C$, the formula is given by:

$$c^2 = a^2 + b^2 - 2ab imes ext{cos}(C)$$