Ta có: $tan\widehat{B} = \dfrac{3}{4}$
⇔ $\dfrac{AC}{AB} = \dfrac{3}{4}$
⇔ $AC = \dfrac{3}{4}AB$
Ta lại có: $AB^{2} + AC^{2} = BC^{2}$ (theo Pytago)
⇔ $AB^{2} + (\dfrac{3}{4}AB)^{2} = (\sqrt{41})^{2}$
⇔ $\dfrac{25AB^{2}}{16} = 41$
⇒ $AB = \sqrt{\dfrac{41.16}{25}} = \dfrac{4\sqrt{41}}{5}$
⇒ $AC = \dfrac{3}{4}AB = \dfrac{3}{4}\cdot\dfrac{4\sqrt{41}}{5} = \dfrac{3\sqrt{41}}{5}$