Solve for c :
x⁴ + cx² + 100 = 0
cx² = -(x⁴ + 100)
c = - (x⁴ + 100)/x²
If x = 0, the right side is undefined and c would have no solution.
Kite Area = (Diagonal 1 * Diagonal 2) / 2
Diagonal 2 = 2 * Kite Area / Diagonal 1
Diagonal 2 =2 * 60 / 15
Diagonal 2 = 120 / 15
Height = 8 inches