> 数学 >
在△ABC中,已知a=2√3,c=√6+√2,B=60°,求b及 A
人气:359 ℃ 时间:2020-10-01 05:48:33
解答
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"
推荐
猜你喜欢
© 2026 79432.Com All Rights Reserved.
电脑版|手机版