Point H is the base of the height drawn from the vertex of the right angle B of triangle ABC to the hypotenuse AC. Find AB if AH = 5, AC = 45

Consider the triangles ABC and ABH.
∠A – general
∠AHB = ∠ABC
Therefore, these triangles are similar (by similarity)
Then AC / AB = AB / AH (the hypotenuse of the large triangle refers to the hypotenuse of the small as the small leg of the large triangle to the small leg of the small triangle)
45 / AB = AB / 5
45 * 5 = AB ^ 2
225 = AB ^ 2
AB = 15
Answer: AB = 15