Question

在Rt△abc中∠c﹦90°BC﹦6，AC﹦8，CD垂直AB于点D。求AB,CD,BD,AD的长

Answer 1

∵∠C=90°,BC=6，AC=8
∴AB=√﹙AC²+BC²)=10
∵CD⊥AB
∴∠ADC=∠BDC=90°
∴S⊿ABC=½×AC×BC=½×AB×CD
∴CD=6×8÷10=4.8
BD=√﹙BC²-CD²)=3.6
AD=10-3.6=6.4

Answer 2

Rt△abc中∠c﹦90°BC﹦6，AC﹦8

所以
AB=√6²+8²=10
CD=6×8÷10=4.8
BD=6²÷10=3.6
AD=10-3.6=6.4

Answer 3

利用勾股定理AB=V(BC^2+AC^2)=10
利用等面积CD=BC*AC/AB=4.8
利用Rt△相似BD=BC^2/AB=3.6, AD=AC^2/AB=6.4

Answer 4

=10

Answer 5

AB=√(BC²+AC²)
=√(6²+8²)
=√(36+64)
=√100
=10

1/2AC*BC=1/2AB*CD
CD=AC*BC/AB
=8*6/10
=48/10
=4.8
BD=√(BC²-CD²)
=√(6²-4.8²)
=√(36-23.04)
=√12.96
=3.6
AD=√(AC²-CD²)
=√(8²-4.8²)
=√(64-23.04)
=√40.96
=6.4