Question

在三角形abc中 a等于根号2 b等于根号三 B等于三分之派 解三角形

Answer 1

(a，b，c)=(√2，√3，(√6+√2)/2)
(A，B，C)=(π/4，π/3，5π/12)
解析：
a=√2，b=√3，C=π/3
使用正弦定理：
(1) 大边对大角
∵a<b
∴A<B=π/3
(2) a/sinA=b/sinB
√2/sinA=√3/sin(π/3)
√2/sinA=2
sinA=√2/2
A=π/4或3π/4(A=3π/4舍去)
由A=π/4，得：C=π-A-B=5π/12
c/sinC=b/sinB
c=bsinC/sinB
c=2sinC
c
=2sin(5π/12)
=2sin75°
=2sin(30°+45°)
=2(sin30°cos45°+cos30°sin45°)
=2(√2/4+√6/4)
=(√6+√2)/2
综上，
(a，b，c)=(√2，√3，(√6+√2)/2)
(A，B，C)=(π/4，π/3，5π/12)

Answer 2

如图

Answer 3

先用正弦定理算出角A,再算出角C，再用正弦定理求出c