LawOfCosines[a_,b_,theta_]:=Sqrt[a^2+b^2-2*a*b*Cos[theta]];
LawOfCosinesDegrees[a_,b_,theta_]:=LawOfCosines[a,b,theta*Pi/180];

(* Exercise 39, p. 481 *)
LawOfCosinesDegrees[2.82,3.56,40.3]

(* Exercise 7, p. 480 *)
LawOfCosinesDegrees[2,8,88]
N[%]

N[%]

(* Exercise 14, p. 480 *)
LawOfCosinesDegrees[60,30,70]
aSide=N[%]

SSA[a_,b_,B_]:=ArcSin[a/b*Sin[B]];
SAA[a_,A_,B_]:=a*Sin[B]/Sin[A];
SSAdegree[a_,b_,B_]:=SSA[a,b,B*Pi/180]*180/Pi;
SAAdegree[a_,A_,B_]:=SAA[a,A*Pi/180,B*Pi/180];

(* now we know SSA, so we can use the law of sines to finish this problem *)

AngleB=SSAdegree[60,aSide,70]

AngleC=180-AngleB - 70

(* Exercise 45, p. 482 *)
LawOfCosinesDegrees[30,50,100]
aSide=N[%]

(* Now to get the bearing: we can use the Law of Sines to get the angle between Egg and Forrest islands: *)
InsideAngle=SSAdegree[50,aSide,100]
Bearing=90-20-InsideAngle
(* S 18.2degrees E *)