We have a triangle triangle ABC and a point K on BC such that AK is an altitude to triangle ABC. If AC = 9, BK = sqrt{5}, and CK = 4, then what is AB?

Use the Pythagorean Theorem to find AK

AK  = sqrt[ AC^2 - CK^2]  =  sqrt [ 9^2  - 4^2]  = sqrt [ 81 - 16]  = sqrt [65]

And we can use it again to find AB

AB = sqrt[ AK^2 + BK^2]  = sqrt[ 65 + 5 ]  = sqrt [70]  ≈ 8.37