Question

已知在三角形ABC中，A=45°，a=2，c=√6，解此三角形

Answer 1

a/sinA = c/sinC => sinC = c * sinA /a = =√6 * √2 / 4 = =√3 /2
C = 60°或 120°

追问

具体过程。

追答

正弦定理 a/sinA = c/sinC = b/SinB ……
A=45°， C=60°， B=75° 或 A=45°， C=120°， B=15°

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b也求一下吧。

追答

A=45°， C=60°， B=75° , sinB = sin(45°+30°) = (1+√3)/(2√2)
a/sinA = b/SinB => b = a sinB / sinA = (1+√3)
A=45°， C=120°， B=15°, sinB = sin(45°- 30°) = (√3-1)/(2√2)
a/sinA = b/SinB => b = a sinB / sinA = ( -1+√3)