△ABC中已知a=2,b=2倍根号2,c=15°.求A?
问题描述：
△ABC中已知a=2,b=2倍根号2,c=15°.求A?
答
cos30°=√3/2,cos15°=√(2+√3)/2
c^2=a^2+b^2-2*a*b*CosC
c^2=4+8-8√2*√(2+√3)/2
=12-4(1+√3)
=8-4√3
c=√6-√2
a^2=b^2+c^2-2*b*c*CosA
4=8+8-4√3-4√2*(√6-√2)*CosA
CosA=(12-4√3)/(8√3-8)
=(3-√3)/(2√3-2)
=√3/2
A=30°