That's an isosceles triangle. We're given the sides and asked for the altitude to the unique base.
The most straightforward solution is with the Pythagorean Theorem. In an isosceles triangle the altitude is also the median, bisecting the side into two each parts, here each 12 feet. That's one leg, the other leg is the unknown altitude, call it a, and the hypotenuse is 18.
[tex]12^2 + a^2 = 18^2[/tex]
[tex]a^2 = 18^2 - 12^2 = 6^2(3^2 - 2^2) = 6^2(5)[/tex]
[tex] a = 6\sqrt{5} [/tex]
Answer: 6√5
