If you know the angle between the equal sides, you can cut it in half with an altitude, then use the sin of that half angle to find the opposite side in the resulting right triangle.

sin (angle) = opposite/hypotenuse, where the hypotenuse is the given length (32 feet). Solve for the opposite side, double it. That's the length of the third side of the isosceles triangle.

For example, what if the angle formed by the equal sides is 50 degrees. Then the altitude forms a right triangle with a base of 1/2 the length the isosceles triangle's third side, and the angle opposite that base 25 degrees.

sin(25) = opposite/32

32*sin(25) = opposite = approximately 13.5 feet. The third side of the isosceles triangle is 2*13.5 = 27 feet.

If the angle is 80 degrees, then the third side is: 2*32*sin(40)= approximately 41 feet.