三角形ABC中,a等于20,B等于45度,C等于30度,解这个三角形.

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A = 180° - (B+C)
sinA=sin[180° - (B+C)]
=sin(B+C)
=sinBcosC + sinCcosB
=√2/2 x √3/2 + 1/2 x √2/2
=(√6+√2)/4
∵a/sinA = b/sinB = c/sinC
∴b = asinB/sinA = 10√2/[(√6+√2)/4] =20√3 - 20
c = asinC/sinA = 10/[(√6+√2)/4] = 10√6 - 10√2