The measure of the missing length AH is 24 units.
Given
In triangle △ABC, ∠ABC=90°, BH is an altitude.
BC=9 and HC=3.
What is the similarity theorem of a triangle?
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
By using the similarity theorem of a triangle:
[tex]\rm \dfrac{HC}{BC}= \dfrac{BC}{AC}\\\\\dfrac{3}{9}=\dfrac{9}{AC}\\\\AC\times 3=9\times 9\\\\3AC=81\\\\AC= \dfrac{81}{3}\\\\AC=27[/tex]
Therefore,
The measure of the missing length AH is;
[tex]\rm AH = AC - HC\\\\AH = 27 - 3\\\\AH = 24\ units[/tex]
Hence, the measure of the missing length AH is 24 units.
To know more about the Similarity theorem click the link given below.
https://brainly.com/question/11977990
