Question

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AC=26 and CH=8, find BH.

Answer 1

12

Explanation:

In the right triangle ABC,

`BC^2=CH\cdot AC.`

Thus,

`BC^2=26\cdot 8=208,\\ \\BC=√(208)=4√(13).`

In the right triangle BHC, by the Pythagorean theorem,

`BC^2=BH^2+CH^2.`

Then

`BH^2=BC^2-CH^2,\\ \\BH^2=(√(208))^2-8^2=208-64=144,\\ \\BH=12.`