Since the ABC triangle is rectangular, and the BH height is drawn from the vertex of the right angle to the hypotenuse, BH^2 = AH * CH.
BH ^ 2 = 36 * 25 = 900.
BH = 30 cm.
In a right-angled triangle ABH, according to the Pythagorean theorem, AB ^ 2 = AH ^ 2 + BH ^ 2 = 1296 + 900 = 2196.
AB = 6 * √61 cm.
In a right-angled triangle BCH, according to the Pythagorean theorem, BC ^ 2 = CH ^ 2 + BH ^ 2 = 625 + 900 = 1525.
BC = 5 * √61 cm.
Answer: BH = 30 cm, AB = AB = 6 * √61 cm, BC = AB = 5 * √61 cm.
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