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# Geometry

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In acute triangle ABC , we know the side lengths AB = sqrt(41) and BC = sqrt($$31$$) and that altitude BD = 5 . What is AC ?

Feb 12, 2022

#1
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What is AC ?

Hello Guest!

Pythagoras twice

$$\overline{AC}=\sqrt{41-25}+\sqrt{31-25}\\ \overline{AC}=\sqrt{16}+\sqrt{6}=4+\sqrt{6}$$

$$\overline{AC}=6.449$$

!

Feb 12, 2022