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We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

 Apr 30, 2024
 #1
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                      A

 

                                      8

 

B        2          K            3            C

 

 

Because AK is an altitude

 

AK   =  sqrt [ AC^2 - CK^2 ]  = sqrt [ 8^2 - 3^2 ] = sqrt [ 55 ]

 

AB =  sqrt [ AK^2 + BK^2 ] =  sqrt [ 55 + 4 ] =  sqrt [ 59 ]

 

 

cool cool cool

 Apr 30, 2024

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