Прямоугольные треугольники

$$\tg A = \frac{BC}{AC} \Rightarrow AC = \frac{BC}{\tg A} = \frac{4}{0,5} = 8$$

$$\tg A = \frac{BC}{AC} \Rightarrow AC = \frac{BC}{\tg A} = \frac{4}{\dfrac{4 \sqrt{33}}{33}} = \sqrt{33}$$

$$AB = \sqrt{AC^2 + BC^2} = \sqrt{(\sqrt{33})^2 + 4^2} = \sqrt{33 + 16} = \sqrt{49} = 7$$

$$A C= \frac{BC}{\tg A} = \frac{BC\cdot \cos A}{\sin A}$$

Вычислим $\sin A$:

$$\sin A = \sqrt{1 - \cos^2A} = \sqrt{1 - \frac{1}{17}} = \frac{4}{\sqrt{17}}$$

Найдём $AC$:

$$AC = \frac{2\cdot\frac{\sqrt{17}}{17}}{\frac{4}{\sqrt{17}}} = 0,5$$

$$\cos^2a = \frac{1 }{1 + \tg^2a} \Rightarrow \cos a = \sqrt{\frac{1}{1+\tg^2 a}}$$

$$AB = \frac{AC}{\cos A} = \frac{4}{\sqrt{\frac{1}{1+\tg^2 A}}} = \frac{4}{\sqrt{\frac{1}{1 + \frac{33}{16}}}} = \frac{4}{\frac{4}{7}} = 7$$

$$BC = AC \cdot \tg A = 8 \cdot 0,5 = 4$$