Question

Question #f3da8

Answer 1

`AD=1/3`

Explanation:

As shown in the diagram, `AE and CD` are the two altitudes.

`DeltaBDC` is a right-angled triangle.
Given `BE=6, EC=8, and BD=9`,
`=> BC=BE+EC=6+8=14`
Let `angleDBC=x`
`cosx=(BD)/(BC)=9/14`

`DeltaABE` is also a right triangle, right-angled at `E`,
`=> ABcosx=6`
`=> AB=6/cosx=6/(9/14)=6xx14/9=28/3`

`AD=AB-BD=28/3-9=1/3`