Ответ: AM=2√S
Объяснение:
S(ΔACM)=S/2 =AC*AM*sin15°/2 => S=AC*AM*sin15° =>AC=S/(AM*sin15°)
По т Пифагора AM²=AC²+CM²
CM=AM*sin15° => AM²=(S/(AM*sin15°))²+(AM*sin15°)²
[tex]AM^4*sin^215-AM^4*sin^415 =S^2\\AM^4= \frac{S^2}{sin^215-sin^415 } =\frac{S^2}{sin^215*cos^215}=\frac{4S^2}{sin^2 30} =16S^2\\ = > AM=2*\sqrt{S}[/tex]
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Ответ: AM=2√S
Объяснение:
S(ΔACM)=S/2 =AC*AM*sin15°/2 => S=AC*AM*sin15° =>AC=S/(AM*sin15°)
По т Пифагора AM²=AC²+CM²
CM=AM*sin15° => AM²=(S/(AM*sin15°))²+(AM*sin15°)²
[tex]AM^4*sin^215-AM^4*sin^415 =S^2\\AM^4= \frac{S^2}{sin^215-sin^415 } =\frac{S^2}{sin^215*cos^215}=\frac{4S^2}{sin^2 30} =16S^2\\ = > AM=2*\sqrt{S}[/tex]