Triangle MNP is an isosceles triangle with sides MN = MP = 3cm. Angle MPN is equal to 72°. The line NQ bisects the angle MNP.
a. Prove that triangles MNP and NPQ are similar.
b. If NP = mcm and PQ = 3 - m, show that m^2 + 3m - 9 = 0.
c. Solve the equation m^2 + 3m - 9 = 0 and find the side length of NP, giving your answer correct to two decimal places.