Question

△ABC的三个内角A、B、C所对的边分别为a、b、c,asinAsinB+bcos^2A=根号2a． 若C^2=b2^+

Answer 1

sinA=asinB

asinAsinB+bcos^2A=√2a

bsin²a+bcos²A=√2a

b=√2a

b^2=2a^2

c^2=b^2+√3a^2

=2a^2+√3a^2

c=a√[2+√3]

=a√[(4+2√3)/2]

=a(√3+1)/√2

cosB=(a^2+c^2-b^2)/(2ac)

=(a^2+2a^2+√3a^2-2a^2)/[2a*(√3+1)a/√2]

=(1+√3)a/√2(√3+1)a

=√2/2

所以 B=45°