In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ab=9, and ac=12, find hc.

Step-by-step explanation:

It is given that in △ABC, ∠ABC=90°, BH is an altitude and AB=9 and AC=12, thus using the Pythagoras theorem in △ABC, we get

Now, From ΔABC and ΔHBC, we have

∠ABC=∠BHC(each90)

∠ACB=∠HCB (Common)

By AA similarity, ΔABC is similar to ΔHBC.

Thus, using the similarity condition, we get

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2