Giải:
a. Tính diện tích tam giác CMN:
Đặt \(S_{CMN}\) là diện tích tam giác CMN.
Ta có: \(S_{ABC} = S_{AMN} + S_{CMN} + S_{BKN}\)
Do đó: \(S_{CMN} = S_{ABC} - S_{AMN} - S_{BKN}\)
Đặt \(S_{AMN} = x\) (cm2).
Ta có: \(S_{AMN} = \frac{1}{2} \cdot AM \cdot AN \cdot \sin{\angle MAN}\)
Do đó: \(x = \frac{1}{2} \cdot AM \cdot AN \cdot \sin{\angle MAN}\)
Đặt \(S_{BKN} = y\) (cm2).
Ta có: \(S_{BKN} = \frac{1}{2} \cdot BK \cdot BN \cdot \sin{\angle BKN}\)
Do đó: \(y = \frac{1}{2} \cdot BK \cdot BN \cdot \sin{\angle BKN}\)
Đặt \(S_{ABC} = 180\) (cm2).
Ta có: \(S_{ABC} = \frac{1}{2} \cdot AB \cdot AC \cdot \sin{\angle BAC}\)
Do đó: \(180 = \frac{1}{2} \cdot AB \cdot AC \cdot \sin{\angle BAC}\)
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