Question

已知在三角形ABC中,cosA=3分之根号6,a、b、c分别是角A、B、C所对的边 ,若sin(90度+B)=（2根号2

Answer 1

作c边上的高CD=h

cosA=√6/3,∴sinA=√(1-6/9)=√3/2,∴ctgA=√2=AD/h

cosB=2√2/3 ∴cosB=√(1-8/9)=1/3,∴ctgB=2√2=BD/h

∴AD/h + BD/h= c/h = √2 + 2√2 =3√2 ∴h=2√2 / 3√2 = 2/3

∴S△ABC=1/2*ch = 2√2/3