Прямоугольные треугольники

$$AB = \frac{BC}{\sin A} = \frac{4}{0,5} = 8$$

$$AC = \frac{BC}{\tg A} = \frac{0,5}{\frac{\sin A}{\sqrt{1-\sin^2 A}}} = \frac{0,5}{\frac{\sqrt{17}/17}{4\sqrt{17}/17}} = \frac{0,5}{\frac{1}{4}} = 2$$

$$AB = \frac{BC}{\sin A} = \frac{4,8}{\sqrt{1-\cos^2 A}} = \frac{4,8}{\sqrt{1-(\frac{7}{25})^2}} = \frac{4,8}{\frac{24}{25}} = 5$$

$$BC = AC \cdot \tg A = 2 \cdot \frac{\sin A}{\sqrt{1 - \sin^2 A}} = 2 \cdot \frac{\frac{\sqrt{17}}{17}}{\sqrt{1 - \frac{17}{289}}} = 2 \cdot \frac{\frac{\sqrt{17}}{17}}{\frac{4\sqrt{17}}{17}} = 2 \cdot \frac{1}{4} = \frac{1}{2} = 0,5$$

$$AB = \frac{AC}{\cos A} = \frac{4}{0,5} = 8$$