✔ 最佳答案
By cosine theorem
AB^2=OA^2+OB^2-2(OA)(OB)cos∠OAB
=25+9-2(5)(3)cos40
=34-30cos40
AB=√(34-30cos40)
^為方便計算 先用計算機AnsM+ (確定Clr左Mem)
OB^2=OA^2+AB^2-2(OA)(AB)cos∠OAB
∠OAB=cos^-1[OB^2-OA^2-AB^2/-2(OA)(AB)]
=cos^-1[9-25-34+30cos40 / -2(5)[√(34-30cos40]
=cos^-1[50-30cos40 / 10√(34-30cos40)
=cos^-1[16+34-30cos40/10√(34-30cos40)
用計算機:cos^-1[16+M^2 / 10M]
∠OAB=35.5(corr.to 3sig.fig.)//