Verified answer

<KEF = 90° - <F = 90° - 60° = 30°, значит

[tex]FK = \frac{1}{2} EF = \frac{1}{2} \times 6 \sqrt{3} = 3 \sqrt{3} [/tex]

По теореме Пифагора:

FK² + EK² = EF²

EK² = EF² - FK²

[tex]EK= \sqrt{ EF {}^{2} - FK {}^{2} } = \sqrt{(6 \sqrt{3}) {}^{2} - (3 \sqrt{3} ) {}^{2} } = \\ \sqrt{36 \times 3 - 9 \times 3} = \sqrt{(36 - 9) \times 3} = \sqrt{27 \times 3} = \\ = \sqrt{ {3}^{2} \times 3 \times 3 } =3 \times 3 = 9[/tex]

По теореме Пифагора:

ED² = DK² + EK²

[tex]ED= \sqrt{DK {}^{2} + EK {}^{2} } = \sqrt{( \sqrt{19}) {}^{2} + {9}^{2} } = \\ = \sqrt{19 + 81} = \sqrt{100} = \sqrt{ {10}^{2} } = 10[/tex]

Ответ: DE = 10 см