16. CB, CD - ?

Угол CBM равен 150 градусам. Следовательно, \(\angle CBA = 180 - 150 = 30\) градусов. В треугольнике ABC угол ACB равен 90 градусам. Следовательно, \(\angle CAB = 180 - 90 - 30 = 60\) градусов. \(\sin(\angle CAB) = \frac{CB}{AB}\) \(\sin(60) = \frac{CB}{18}\) \(\frac{\sqrt{3}}{2} = \frac{CB}{18}\) \(CB = 9\sqrt{3}\) \(\cos(\angle CBA) = \frac{CB}{BM}\) \(\cos(30) = \frac{9\sqrt{3}}{BM}\) \(\frac{\sqrt{3}}{2} = \frac{9\sqrt{3}}{BM}\) \(BM = 18\) \(\tan(\angle CBA) = \frac{AC}{CB}\) \(\tan(30) = \frac{AC}{9\sqrt{3}}\) \(\frac{1}{\sqrt{3}} = \frac{AC}{9\sqrt{3}}\) \(AC = 9\) \(\tan(\angle CAB) = \frac{CB}{AC}\) \(\tan(60) = \frac{9\sqrt{3}}{AC}\) \(\sqrt{3} = \frac{9\sqrt{3}}{AC}\) \(AC = 9\) В треугольнике ACD угол ADC равен 90 градусам. \(\cos(\angle CAB) = \frac{AD}{AB}\) \(\cos(60) = \frac{CD}{AC}\) \(\frac{1}{2} = \frac{CD}{9}\) \(CD = 4.5\) Ответ: \(CB = 9\sqrt{3}\), CD = 4.5