In triangle ABC, the angle ABC = 90 degrees, and BH is an altitude. Find segment HC if segment AB = 9 and segment AC = 12.
Since angle ABC is 90 degrees, triangle ABC is a right triangle.
Using the Pythagorean theorem, we can find the length of segment BC:
BC^2 = AB^2 + AC^2
BC^2 = 9^2 + 12^2
BC^2 = 81 + 144
BC^2 = 225
BC = 15
Since BH is an altitude, triangle AHC is also a right triangle.
Using the Pythagorean theorem again, we can find the length of segment HC:
HC^2 = AC^2 - AH^2
HC^2 = 12^2 - 9^2
HC^2 = 144 - 81
HC^2 = 63
HC ≈ √63
HC ≈ 7.94
Therefore, segment HC is approximately 7.94.