Two new formulas for adjusting shooting angle in the technique of shooting method were formulated. These formulas are modified Newton's formula and a Cubic Newton's formula which were obtained to form Taylor series. The effectiveness of these formulas were investigated by solving two different nonlinear boundary value problems, the results obtained were compared with the regular Newton's formula and both the new methods performed better that the Newton's method with the Cubic having the best performance. This inference is evident from the table of errors, tolerance value which is the absolute difference between two successive iterations also gave credence to the performance of the two formulas.