Question

在三角形abc中.已知a=2,b=2根号2,C=15°,求角A、B和边c的值

Answer 1

cos15=cos(45-30)

=cos45cos30+sin45sin30

=(√6+√2)/4

c²=a²+b²-2abcosC

=4+8-8√2*(√6+√2)/4

=12-4√3-4

=8-2√12

=(√6-√2)²

c=√6-√2

sin15=sin(45-30)=sin45cos30-cos45sin30=(√6-√2)/4

a/sinA=c/sinC

2/sinA=(√6-√2)/[(√6-√2)/4]=4

sinA=1/2

因为a