Question

在三角形ABC中，角A=45度，a=2，c=根号6，解此三角形，要求过程

Answer 1

解：A
=
π/4
，a
=
2
，c
=
√6
，有正弦定理可得
a/sinA
=
c/sinC
=
b/sinB
=>
2/sin(π/4)
=
(√6)/
sinC
=>
sinC
=
√3/2
=>
C
=
π/3
或者
2π/3
=>
B
=
π
-
A
–
C
=
5π/12
或者
π/12
=>
b
=
asinB/sinA
=
2sinB/sin(π/4)
=
2√2sinB
=
1
+
√3
或者√3
–
1
，所以
(a，b，c)
=
(2，1
+
√3，√6)
，(A，B，C)
=
(π/4，5π/12，π/3)
或者
(a，b，c)
=
(2，√3
–
1，√6)
，(A，B，C)
=
(π/4，π/12，2π/3)
。（一共有
两解
）