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 $AB$?
A
8
B 2 K 3 C
Because AK is an altitude, we can manipulate the Pythagorean Theorem twice
AK = sqrt [ AC^2 - CK^2 = sqrt [ 8^2 - 3^2 ] = sqrt [ 55]
AB = sqrt [ AK^2 + BK^2 ] = sqrt [ 55 + 4 ] = sqrt [ 59 ]
+1439 
