Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 738

\[1)\ a = 6\ см:\]

\[p = \frac{1}{2}(a + a + a) = \frac{3a}{2} =\]

\[= \frac{3 \bullet 6}{2} = 3 \bullet 3 = 9\ (см).\]

\[S = \frac{1}{2} \bullet a \bullet a \bullet \sin{60{^\circ}} = \frac{a^{2}}{2} \bullet \frac{\sqrt{3}}{2} =\]

\[= \frac{6^{2} \bullet \sqrt{3}}{4} = \frac{36\sqrt{3}}{4} = 9\sqrt{3}\ \left( см^{2} \right).\]

\[S = p \bullet r:\]

\[r = \frac{S}{p} = \frac{9\sqrt{3}}{9} = \sqrt{3}\ (см);\]

\[d = 2r = 2\sqrt{3}\ (см).\]

\[Ответ:\ \ 2\sqrt{3}\ см.\]

\[2)\ a = 4\ см:\]

\[\text{tg}\frac{\alpha}{2} = \frac{4,5\text{/}2}{a} = \frac{2,25}{4} = \frac{9}{16};\]

\[\alpha = 2\ arctg\frac{a}{2} = 2\ arctg\frac{9}{16};\]

\[a \approx 2 \bullet 29,36{^\circ} \approx 58,72{^\circ}.\]

\[Ответ:\ \ 2\ arctg\frac{9}{16} \approx 58,72{^\circ}.\]