12 MN, ZKMN, ZN-?

Ответ: MN = 28, ∠KMN = 30°, ∠N = 30°

1. Шаг 1: Найдем ∠MKT.

\[\angle MKT = 180^\circ - 120^\circ = 60^\circ\]

2. Шаг 2: Найдем ∠KMT.

\[\angle KMT = 90^\circ - \angle MKT = 90^\circ - 60^\circ = 30^\circ\]

3. Шаг 3: Найдем MT.

\[\sin(\angle MKT) = \frac{MT}{MK} \Rightarrow MT = MK \cdot \sin(\angle MKT) = 14 \cdot \sin(60^\circ) = 14 \cdot \frac{\sqrt{3}}{2} = 7\sqrt{3}\]

4. Шаг 4: Найдем KT.

\[\cos(\angle MKT) = \frac{MK}{KT} \Rightarrow KT = \frac{MK}{\cos(\angle MKT)} = \frac{14}{\cos(60^\circ)} = \frac{14}{\frac{1}{2}} = 28\]

5. Шаг 5: Найдем ∠KMN.

\[\angle KMN = \frac{180^\circ - 120^\circ}{2} = 30^\circ\]

6. Шаг 6: Найдем MN.

\[MN = 2 \cdot MK \cdot \cos(30^\circ) = 28\]

7. Шаг 7: Найдем ∠N.

\[\angle N = \angle KMN = 30^\circ\]

Ответ: MN = 28, ∠KMN = 30°, ∠N = 30°