Question

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

Answer 1

Answer: AH = 24 unit

Step-by-step 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,

$\frac{AC}{BC} = \frac{BC}{HC}$

$AC = BC\times \frac{BC}{HC}$

$AC = \frac{BC^2}{HC}$

Here,  BC = 9 unit  and HC = 3 unit,

$AC = \frac{9^2}{3}=\frac{81}{3}=27$

Since, by the below diagram,

AH = AC - HC

AH = 27 - 3

AH = 24 unit