64 = 2 * 2 * 2 * 2 * 2 * 2
48 = 2 * 2 * 2 * 2 * 3
56 = 2 * 2 * 2 * 7
24 = 2 * 2 * 2 * 3
28 = 2 * 2 * 7
128 = 2 * 2 * 2 * 2 * 2 * 2 * 2
78 = 2 * 3 * 13
256 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
625 = 5 * 5 * 5 * 5
1) По основному тригонометрическому тождеству
![cosA= \sqrt{1-sin^2A} = \sqrt{1-( \frac{3}{5})^2 }= \frac{4}{5}](https://tex.z-dn.net/?f=cosA%3D+%5Csqrt%7B1-sin%5E2A%7D+%3D+%5Csqrt%7B1-%28+%5Cfrac%7B3%7D%7B5%7D%29%5E2+%7D%3D+%5Cfrac%7B4%7D%7B5%7D+)
2)
![cosA= \frac{AC}{AB} = \frac{4}{5}](https://tex.z-dn.net/?f=cosA%3D+%5Cfrac%7BAC%7D%7BAB%7D+%3D+%5Cfrac%7B4%7D%7B5%7D+)
По условию АС=3, поэтому
![\frac{3}{AB} = \frac{4}{5}](https://tex.z-dn.net/?f=+%5Cfrac%7B3%7D%7BAB%7D+%3D+%5Cfrac%7B4%7D%7B5%7D+)
AB=3,75
3) По т.Пифагора
![BC= \sqrt{AB^2-AC^2} = \sqrt{3,75^2-3^2} =2,25](https://tex.z-dn.net/?f=BC%3D+%5Csqrt%7BAB%5E2-AC%5E2%7D+%3D+%5Csqrt%7B3%2C75%5E2-3%5E2%7D+%3D2%2C25)
Ответ: 2,25.