samuelerlikhman samuelerlikhman
  • 02-02-2019
  • Mathematics
contestada

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

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frika
frika frika
  • 17-02-2019

Answer:

12

Step-by-step explanation:

In the right triangle ABC,

[tex]BC^2=CH\cdot AC.[/tex]

Thus,

[tex]BC^2=26\cdot 8=208,\\ \\BC=\sqrt{208}=4\sqrt{13}.[/tex]

In the right triangle BHC, by the Pythagorean theorem,

[tex]BC^2=BH^2+CH^2.[/tex]

Then

[tex]BH^2=BC^2-CH^2,\\ \\BH^2=(\sqrt{208})^2-8^2=208-64=144,\\ \\BH=12.[/tex]

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