Question

在三角形ABC中,角C=90度,AC=6,BC=8,四边形DEFG是它的内接矩形,点D在边AC上,点E,F在AB上,点G

Answer 1

相信LZ自己已经画图了吧,我就不发图了

(1)

CD=x,GB=y,AD=6-x,AB=√(AC^2+BC^2)=10

sinB=AC/AB=GF/y

GF/y=6/10

GF=3y/5

∵DEFG为矩形

∴DE=GF=3y/5

sinA=BC/AB=(3y/5)/(6-x)

4/5=(3y/5)/(6-x)

y=(24-4x)/3

(2)

cosB=BC/AB=BF/GB

8/10=BF/y

BF=4y/5=