110 
Example 1. Given a — 2.903, B = 79° eo @ =) 33° 152 sComputeyAs— 
67° 5’ and log } = 0.49146, 6 = 3.1007, log c = 0.23 757, c = 1.7281, by the law 
of sines. 
CHECKS 
(b-c) cos 4A — a sin BG) 
0.13754 0.46285 
bl 1007 9 .92090—-10 9.59558-10 
6 — aol oe oe 
0.05844 0.05843 
b+c = 4.8288 (+c) sin 4A =a cos %(B-C) 
jp = 1 27 0.68384 0.46285 
Bi — e400" 9 .74236-10 9 .96335-10 
(Ola BBE aby —_—_—_— ——_— 
0.42610 0.42610 
B-C' = 46° 25’ (b+c) (b-c) sin A = a? sin (B-C) 
16(B—-C) = 23° 127.5 0.68384 0.46285 
0.13754 0.46285 
WA i= Sooo oO 9.96429-10 9.85996-10 
0.78567 0.78566 
Case 2. Given two sides and their included angle. 
Example 1. a = 22, 6b = 12, C = 42°. Compute c = 15.350 by the law of 
cosines. 
CHECK 
; aa 22 s (s—c) tan? 4C = (s—a) (s—b) 
c = 15.350 1.39226 
0.96965 
2s = 49.350 9.58418-10 0.42732 
Si=——924 Gro 9.58418-10 1.10295 
s—a — 2,675 1.53027 1.53027 
s—b = 12.675 
S-c = 9.325 
Check = 24.675 
Compute A = 106° 27’.7 and B = 31° 32’.4 by law of sines. 
CHECKS 
a+b = 34 (a—b) cos 4C = c sin %(A-B) 
a-b = 10 
1.00000 1.18611 
Co — eto 9.97015-10 9.78405-10 
0.97015 0.97016 
A=) 106° 2757 
(a+ b) sin %C = c cos 4(A-B) 
i3} == Sul splert 
—_———— — 1.53148 1.18611 
A-—B = 74° 53’.3 9 .55433-10 9 .89970—10 
1.08581 1.08581 
i CA—5) ——"o1 1 2 eo 
(a+b) (a—b) sin C = c? sin (A—B) 
YC = 21° 
1.53148 1.18611 
1.00000 1.18611 
9.82551-10 9 .98478-10 
2.53699 2.53700 
Example 2. Given a = 34.645, b = 22.531, C = 43° 31’. 
@ = 34.645 1 C—O ese 4(A+B) = 68° 14’.5 
b= 22 bel Then compute 144(A—-B) = 27° 57’'.6 
a+b = 57.176 whence Ay—— 06> ebZrl 
a—b = 12.114 and B = 40° 16’.9 
