Answer: AH = 24 unit
Step-by-step explanation:
Since, in triangles ABC and BHC,
[tex]m\angle ABC\cong m\angle BHC[/tex] ( Right angles)
[tex]m\angle BCA\cong m\angle HCB [/tex] ( Reflexive )
Hence, By AA similarity postulate,
[tex]\triangle ABC\sim\triangle BHC[/tex]
By the property of similar triangle,
[tex]\frac{AC}{BC} = \frac{BC}{HC}[/tex]
[tex]AC = BC\times \frac{BC}{HC}[/tex]
[tex]AC = \frac{BC^2}{HC}[/tex]
Here, BC = 9 unit and HC = 3 unit,
[tex]AC = \frac{9^2}{3}=\frac{81}{3}=27[/tex]
Since, by the below diagram,
AH = AC - HC
AH = 27 - 3
AH = 24 unit
