In triangle ABC, the angle ABC = 90 degrees, and BH is an altitude. Find segment BH if segment AH = 4 and segment HC = 1.
Since BH is an altitude of triangle ABC, it divides the triangle into two right triangles, triangle ABH and triangle CBH.
Using the Pythagorean theorem in triangle ABH, we have:
BH^2 + AH^2 = AB^2
BH^2 + 4^2 = AB^2
BH^2 + 16 = AB^2
Similarly, in triangle CBH, we have:
BH^2 + HC^2 = CB^2
BH^2 + 1^2 = CB^2
BH^2 + 1 = CB^2
Since angle ABC = 90 degrees, AB is the hypotenuse of triangle ABH and CB is the hypotenuse of triangle CBH, which means AB = CB.
So, we have:
BH^2 + 16 = AB^2
BH^2 + 16 = CB^2
BH^2 + 16 = BH^2 + 1
Subtracting BH^2 from both sides:
16 = 1
This is a contradiction, so there must be a mistake in the given information.