Question

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.

Answer 1

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