Using the Law of Cosines, we can solve for x:

MT^2 = MH^2 + AT^2 - 2(MH)(AT)cos(m<HMA)

Substituting in the given values:

14^2 = (2x - 6)^2 + (x + 3)^2 - 2(2x - 6)(x + 3)cos(115°)

Simplifying and solving for x:

196 = 4x^2 - 24x + 36 + x^2 + 6x + 9 - 2(2x^2 - 6x + 3x - 18)cos(115°)

196 = 5x^2 - 18x + 45 + 36cos(115°)

5x^2 - 18x - 151.54 = 0

Using the quadratic formula:

x = [18 ± sqrt(18^2 - 4(5)(-151.54))] / (2(5))

x = [18 ± sqrt(4576.8)] / 10

x = 14.22 or x = -2.68

Since we cannot have a negative length, we reject x = -2.68 and conclude that:

x = 14.22

Therefore, MH = (2x - 6) cm = 22.44 cm and AT = (x + 3) cm = 17.22 cm.