Question

在△ABC中,已知a=2√3,c=√6+√2,B=60°,求b及 A

Answer 1

由 b²=a²+c²-2ac cos B 代入得：
b²=(2√3)²+(√6)²-2(2√3)(√6) cos 60°
=12+6-12(√2)(1/2)
=18-6√2
b=√(18-6√2)
由 a/sinA=b/sinB 代入得：
2√3/sinA=√(18-6√2)/sin 60°
√(18-6√2)sinA=2√3)(√3/2)=3
sinA=3/√(18-6√2)
=3√(18+6√2)/√[18²-(6√2)²]
=3√(18+6√2)/√(324-72)
=3√(18+6√2)/√252
=3√(18+6√2)/3√28
=√(18+6√2)/√28
=√[(18+6√2)/28]
=√[(9+3√2)/14]
=0.97257539873410641492864696478185......
A=76.550524473863696546269072643024......°
=76°33.031468431821792776144358581446......'
=76°33'1.8881059093075665686615148867356......"
≈76°33'2"