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

 Dec 22, 2021
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" such that AK in altitude to ABC."

I'm assuming this means that AK is an altitude to BC. I suggest drawing a diagram.

If CK = 4 and AC = 9, then by the Pythagorean Theorem, AK^2 = 9^2-4^2 = 65, so AK = √65. Since BK is √5, AB^2 = 65 + 5 = 70, so AB = √70.

 Dec 22, 2021

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