$\begin{array}{l} A{B^2} = A{H^2} + B{H^2} = 881\\ \Rightarrow AB = \sqrt {881} \left( {cm} \right)\\ \dfrac{1}{{A{H^2}}} = \dfrac{1}{{A{B^2}}} + \dfrac{1}{{A{C^2}}}\\ \Rightarrow A{C^2} = 360,8576 \Rightarrow AC \approx 19\left( {cm} \right)\\ A{H^2} = HB.HC \Leftrightarrow {16^2} = 25.HC \Rightarrow HC = 10,24\left( {cm} \right)\\ BC = BH + HC = 25 + 10,24 = 35,24\left( {cm} \right) \end{array}$