3. MN = 36 MP, PN - ?

Рассмотрим треугольник $$\triangle MNP$$. Угол $$\angle M = 30^{\circ}$$. $$\sin(30^{\circ}) = \frac{PN}{MN}$$ $$\frac{1}{2} = \frac{PN}{36}$$ $$PN = \frac{36}{2} = 18$$ $$\cos(30^{\circ}) = \frac{MP}{MN}$$ $$\frac{\sqrt{3}}{2} = \frac{MP}{36}$$ $$MP = \frac{36\sqrt{3}}{2} = 18\sqrt{3}$$ Ответ: $$PN = 18$$, $$MP = 18\sqrt{3}$$