已知如图在Rt△ABC中,∠ABC=90º,AB=4,sin∠BAC=3/5,P是边AC上的一点……九上期中考试题
2个回答
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(1)
设∠BAC=α
sinα=BC/AC=3/5
BC=3/5AC
AB=4
AB^2+BC^2=AC^2
16+9/25AC^2=AC^2
AC^2=25
AC=5
BC=3
(2)
AD∥BC,BC⊥AB
AD⊥AB
DP⊥AC
△ABC∽△ADP
AD/AC=AP/BC
AC=5,BC=3,AP=x
AD=5/3x
△ADE中AD∥BC
BC/AD=BE/AE
BC=3,AE=BE+AB=BE+4,BE=y
3/(5/3x)=y/(y+4)
5/3xy=3y+12
y=36/(5x-9)
(3)
当AD=DC时
AP=1/2AC=5/2
BE=36/(5x5/2-9)
BE=72/7
当AD=AC时
AP=3,AD=AC=5
BE=36/(5x3-9)=6
设∠BAC=α
sinα=BC/AC=3/5
BC=3/5AC
AB=4
AB^2+BC^2=AC^2
16+9/25AC^2=AC^2
AC^2=25
AC=5
BC=3
(2)
AD∥BC,BC⊥AB
AD⊥AB
DP⊥AC
△ABC∽△ADP
AD/AC=AP/BC
AC=5,BC=3,AP=x
AD=5/3x
△ADE中AD∥BC
BC/AD=BE/AE
BC=3,AE=BE+AB=BE+4,BE=y
3/(5/3x)=y/(y+4)
5/3xy=3y+12
y=36/(5x-9)
(3)
当AD=DC时
AP=1/2AC=5/2
BE=36/(5x5/2-9)
BE=72/7
当AD=AC时
AP=3,AD=AC=5
BE=36/(5x3-9)=6
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