Question

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. BC=9 and HC=3, find AH.

Answer 1

24

Explanation:

Answer 2

Answer: AH = 24 unit

Explanation:

Since, in triangles ABC and BHC,

`m\angle ABC\cong m\angle BHC` ( Right angles)

`m\angle BCA\cong m\angle HCB` ( Reflexive )

Hence, By AA similarity postulate,

`\triangle ABC\sim\triangle BHC`

By the property of similar triangle,

`(AC)/(BC) = (BC)/(HC)`

`AC = BC* (BC)/(HC)`

`AC = (BC^2)/(HC)`

Here, BC = 9 unit and HC = 3 unit,

`AC = (9^2)/(3)=(81)/(3)=27`

Since, by the below diagram,

AH = AC - HC

AH = 27 - 3

AH = 24 unit