Решебник по геометрии 7 класс Атанасян ФГОС Задание 1060

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Год:2020-2021-2022
Тип:учебник

Задание 1060

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Геометрия 7 класс Атанасян ФГОС Просвещение
 
фгос Геометрия 7 класс Атанасян ФГОС, Бутузов Просвещение
Издание 1
Геометрия 7 класс Атанасян ФГОС Просвещение

\[\boxed{\mathbf{1060.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\textbf{а)}\ AB = 8\ см;\ \angle A = 30{^\circ};\ \]

\[\angle B = 45{^\circ}:\]

\[1)\ \angle C = 180{^\circ} - (30{^\circ} + 45{^\circ}) =\]

\[= 180{^\circ} - 75{^\circ} = 105{^\circ}.\]

\[2)\ По\ теореме\ синусов:\]

\[\frac{\text{AB}}{\sin{\angle C}} = \frac{\text{AC}}{\sin{\angle B}} = \frac{\text{BC}}{\sin{\angle A}}\]

\[\frac{8}{\sin{105{^\circ}}} = \frac{\text{AC}}{\sin{45{^\circ}}}\]

\[AC = \frac{8\sin{45{^\circ}}}{\sin{105{^\circ}}} = \frac{8 \bullet \frac{\sqrt{2}}{2}}{0,9659} =\]

\[= 5,8564\ см.\]

\[\frac{8}{\sin{105{^\circ}}} = \frac{\text{BC}}{\sin{30{^\circ}}}\]

\[BC = \frac{8\sin{30{^\circ}}}{\sin{105{^\circ}}} = \frac{8 \bullet \frac{1}{2}}{0,9659} =\]

\[= 4,1411\ см.\]

\[\textbf{б)}\ AB = 5\ см;\ \angle C = 60{^\circ};\ \]

\[\angle B = 45{^\circ}:\]

\[1)\ \angle A = 180{^\circ} - (60{^\circ} + 45{^\circ}) =\]

\[= 180{^\circ} - 105{^\circ} = 75{^\circ}.\]

\[2)\ По\ теореме\ синусов:\]

\[\frac{\text{AB}}{\sin{\angle C}} = \frac{\text{AC}}{\sin{\angle B}} = \frac{\text{BC}}{\sin{\angle A}}\]

\[\frac{5}{\sin{105{^\circ}}} = \frac{\text{AC}}{\sin{45{^\circ}}}\]

\[AC = \frac{5\sin{45{^\circ}}}{\sin{60{^\circ}}} = 4,1\ см.\]

\[\frac{5}{\sin{105{^\circ}}} = \frac{\text{BC}}{\sin{75{^\circ}}}\]

\[BC = \frac{5\sin{75{^\circ}}}{\sin{60{^\circ}}} = 5,58\ см.\]

\[\textbf{в)}\ AB = 3\ см;BC = 3,3\ см;\]

\[\angle A = 48{^\circ}30^{'}:\]

\[1)\ По\ теореме\ синусов:\]

\[\frac{\text{AB}}{\sin{\angle C}} = \frac{\text{AC}}{\sin{\angle B}} = \frac{\text{BC}}{\sin{\angle A}}\]

\[\frac{3}{\sin{\angle C}} = \frac{3,3}{\sin{48{^\circ}30^{'}}}\]

\[\sin{\angle C} = \frac{3\sin{48{^\circ}30^{'}}}{3,3} =\]

\[= \frac{0,749}{1,1} = 0,6809\]

\[\angle C = 42{^\circ}55^{'}.\]

\[\frac{3,3}{\sin{48{^\circ}30^{'}}} = \frac{\text{AC}}{\sin{88{^\circ}35^{'}}}\]

\[AC = \frac{3,3\sin{88{^\circ}35^{'}}}{\sin{48{^\circ}30^{'}}} =\]

\[= \frac{3,3 \bullet 0,9997}{0,749} = 4,4\ см.\]

\[2)\ \angle B =\]

\[= 180{^\circ} - \left( 42{^\circ}55^{'} + 48{^\circ}30^{'} \right) =\]

\[= 88{^\circ}35^{'}.\]

\[\textbf{г)}\ AC = 10,4\ см;BC = 5,2\ см;\]

\[\angle B = 62{^\circ}48^{'}:\]

\[1)\ По\ теореме\ синусов:\]

\[\frac{\text{AB}}{\sin{\angle C}} = \frac{\text{AC}}{\sin{\angle B}} = \frac{\text{BC}}{\sin{\angle A}}\]

\[\frac{10,4}{\sin{62{^\circ}48^{'}}} = \frac{5,2}{\sin{\angle A}}\]

\[\sin{\angle A} = \frac{5,2\sin{62{^\circ}48^{'}}}{10,4} =\]

\[= \frac{5,2 \bullet 0,8894}{10,4} = 0,4447\]

\[\angle A = 26{^\circ}24^{'}.\]

\[\frac{10^{'}4}{\sin{62{^\circ}48^{'}}} = \frac{\text{AB}}{\sin{90{^\circ}48^{'}}}\]

\[AB = \frac{10,4\sin{90{^\circ}48^{'}}}{\sin{62{^\circ}48^{'}}} =\]

\[= \frac{10,4 \bullet 0,9999}{0,8894} = 11,69\ см.\]

\[2)\ \angle C =\]

\[= 180{^\circ} - \left( 62{^\circ}48^{'} + 26{^\circ}24^{'} \right) =\]

\[= 90{^\circ}48^{'}.\]

Издание 2
фгос Геометрия 7 класс Атанасян ФГОС, Бутузов Просвещение

\[\boxed{\mathbf{1060.еуроки - ответы\ на\ пятёрку}}\]

\[Рисунок\ по\ условию\ задачи:\]

\[\mathbf{Дано:}\]

\[A( - 2; - 2);\]

\[B( - 3;1);\]

\[C(7;7);D(3;1)\]

\[MN - средняя\ линия.\]

\[\mathbf{Написать:}\]

\[уравнения\ прямых\]

\[\textbf{а)}\ \text{AC\ }и\ BD;\]

\[\textbf{б)}\ MN.\]

\[\mathbf{Решение.}\]

\[\textbf{а)}\ 1)\ A( - 2; - 2):\]

\[ax + by + c = 0;\]

\[a \bullet ( - 2) + b \bullet ( - 2) + c = 0;\]

\[- 2a - 2b + c = 0;\ \]

\[- 2a = 2b - c;\]

\[a = \frac{c - 2b}{2} = \frac{c}{2} - b.\]

\[C(7;7):\]

\[ax + by + c = 0;\]

\(7a + 7b + c = 0;7a = - 7b - c;\)

\[a = \frac{- 7b - c}{7} = - b - \frac{c}{7};\]

\[- b - \frac{c}{7} = \frac{c}{2} - b\]

\[\left\{ \begin{matrix} c = 0 \\ a = - b \\ \end{matrix} \right.\ .\]

\[2)\ Уравнение\ прямой\ AC:\]

\[\left. \ ax - ay + 0 = 0\ \ \ \ \ \ \ \ \right|:a\]

\[x - y = 0.\]

\[3)\ B( - 3;1):\]

\[ax + by + c = 0;\]

\[- 3a + b + c = 0;\]

\[a = \frac{b + c}{3}.\]

\[D(3;1):\]

\[ax + by + c = 0;\]

\[3a + b + c = 0;\]

\[b = - 3a - c;\]

\[a = \frac{- 3a - c + c}{3} = - a\]

\[a = 0 \Longrightarrow b = - c.\]

\[4)\ Уравнение\ прямой\ BD:\]

\[ax + by + c = 0\]

\[- cy + c = 0\ \ \ \ |\ :c\]

\[- y + 1 = 0.\]

\[3)\ N(5;4):\]

\[5a + 4b + c = 0\]

\[a = \frac{- 4b - c}{5}.\]

\[M( - 2,5; - 0,5):\ \]

\[\left. \ - \frac{5}{2}a - \frac{1}{2}b + c = 0 \right| \bullet 2\]

\[- 5a - b + 2c = 0;b = 2c - 5a\]

\[b = 2c - ( - 4b + c) =\]

\[= 2c + 4b + c + 4b\]

\[- 3b = 3c\]

\[b = - c \Longrightarrow a = \frac{3}{5}\text{c.}\]

\[4)\ Уравнение\ прямой\ MN:\]

\[\left. \ \frac{3}{5}cx - cy + c = 0 \right| \bullet \frac{5}{c}\]

\[3x - 5y + 5 = 0.\]

\[Ответ:\ а)\ x - y =\]

\[= 0\ и\ - y + 1 = 0;\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ б)\ 3x - 5y + 5 = 0.\]

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