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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 8 and AD 2, what is the length of AC? (Note: the figure is not drawn to scale.) B 8 А 2 D C Answer: Submit Answer FR Type here to search O

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Solution

For this case we can start solving for BD like this:

[tex]BD=\sqrt[]{8^2-2^2}=\sqrt[]{60}=2\sqrt[]{15}[/tex]

Now we can create two equations:

[tex](2+DC)^2=64+BC^2[/tex][tex]BC^2=60+DC^2[/tex]

Replacing the second equation in the first one we got:

[tex](2+DC)^2=64+60+DC^2[/tex]

Solving for DC we have:

[tex]4+4DC+DC^2=124+DC^2[/tex][tex]4DC=120[/tex]

DC= 120/4 = 30

Then the final answer would be:

AC= AD + DC = 2+ 30 =32