Assuming all angles are to be calculated. Using the cosine rule: a^2=b^2+c^2-2bc(cos(A)) => cos(A)=(b^2+c^2-a^2)/(2bc) substitute values, cos(A)=(17^2+19^2-22^2)/(2*17*19)=83/323=0.25697 A=75.11 degrees similarly cos(B)=(19^2+22^2-17^2)/(2*19*22)=139/209=0.66507 B=48.31 degrees cos(C)=(22^2+17^2-19^2)/(2*22*17)=103/187=0.55080 C=56.58 degrees Check: (75.11+48.31+56.58)=180.00 degrees, ok.
Note: 1. Better accuracy than required is calculated for a more accurate check. You need to round answers to the specified accuracy. 2. In fact, not all tables are made from formulas. Some tables are compiled by experimentation and require hundreds and thousands of man-years to complete (e.g. steam tables).
