110 



67 _ . 

 of sines 



Example 1. Given a = 

 5' and log b = 0.49146, b 



2.903, B = 79° 4C'. C = 33° 15' 

 := 3.1007, log c = 0.23757, C = ] 



Compute A = 

 r281, by the law 



6 == 3 . 1007 

 c = 1.7281 



&+C = 4.8288 



6-C = 1 . 3726 

 B = 79° 40' 

 C =^ 33° 15' 



B-C = 46° 25' 



J^(B-C) = 23° 12'.5 



J^A = 33° 32' 5 



Case 2. Given two sides 



Example 1. a = 22, b 

 cosines. 



a = 22 

 5 = 12 

 c = 15.350 



(6-c) cos 

 0.13754 

 9.92090-10 



Checks 



i^A = a sin 14(3-0 



0.46285 

 9.59558-10 



. 05844 



(&+C) sin HA 



. 68384 

 9.74236-10 



0.05843 

 a cos }4(B-C) 



. 46285 

 9 . 96335-10 



0.42610 



(b+c) 

 . 68384 



0.13754 

 96429-10 



0.42610 



a2 sin (B-C) 



0.46285 

 . 46285 

 9.85996-10 



2s = 49.350 

 s = 24.675 



S-a = 2.675 

 S-b = 12.675 

 S-C = 9.325 



Check = 24.675 



0.78567 

 and their included angle. 

 = 12, C = 42°. Compute c 



Check 

 s is-c) tan2 i^c = {s-a) {s-b) 



1.39226 

 0.96965 

 9.58418-10 

 9.58418-10 



0.78566 

 15.350 by the law of 



. 42732 

 1 . 10295 



1 . 53027 



Compute A = 106° 27'. 7 and B 



a+& = 34 

 a-b r= 10 



106° 27'.7 

 31° 32'.4 



A-B = 74° 53'.3 



= 31° 32'.4 by law of sines. 

 Checks 



{a-b) cos J^C = c sin ^{A-B) 



1 . 00000 

 9.97015-10 



0.97015 



{a+ b) sin 



.53148 

 .55433-10 



H(A-B) = 37° 27'.G 

 iAC = 21° 



{a+b) {a-b) sin C =^ c^- sin (A-B) 



1.53148 

 1 . 00000 

 9.82551-10 



1.18611 

 1.18611 

 9.98478- 



Example 2. Given a = 34.645, 6 = 22.531, C = 43° 31'. 



a = 34.645 ViC = 21° 45'.5 y2{A+B) = 68° 14'.5 



b = 22.531 Then compute y2{A-B) = 27° 57'.6 



a+b = 57.176 

 a-b = 12.114 



whence 

 and 



A = 96° 12'.1 

 B = 40° 16'.9 



