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Консультация № 196748
21.10.2019, 14:58
0.00 руб.
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3
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Дан равносторонний треугольник ABC. Точки M и K принадлежат сторонам AC и BC соответственно. CM=AM/2, CK=BK/2. Отрезки AK и BM пересекаются в точке L. Найдите угол CLB.
Дан равносторонний треугольник ABC. Точки M и K принадлежат сторонам AC и BC соответственно. CM=AM/2, CK=BK/2. Отрезки AK и BM пересекаются в точке L. Найдите угол CLB.
Обсуждение
21.10.2019, 19:47
общий
Адресаты:
Я предлагаю Вам самостоятельно выполнить рисунок к задаче и показать в мини-форуме консультации.
Об авторе:
Facta loquuntur.
Facta loquuntur.
25.10.2019, 12:36
общий
это ответ
Здравствуйте, 1234aaa!
Если не задаваться целью получить решение задачи в радикалах, то искомую величину угла можно вычислить следующим образом. Воспользуемся рисунком, который Вы прикрепили к сообщению в мини-форуме консультации. Согласно ему имеем
по теореме косинусов
По теореме синусов
-- искомая величина угла.
Можно, однако, получить значение косинуса искомого угла в радикалах и по нему вычислить искомую величину угла. Для этого воспользуемся тем, что по теореме синусов
а по теореме косинусов
тогда
то есть
или
но последнее решение не подходит, потому что угол
должен быть тупым.
Итак,
Литература
Погорелов А. В. Геометрия. Учебник для 7 -- 11 классов общеобразовательных учреждений. -- М.: Просвещение, 1995. -- 383 с.
Если не задаваться целью получить решение задачи в радикалах, то искомую величину угла можно вычислить следующим образом. Воспользуемся рисунком, который Вы прикрепили к сообщению в мини-форуме консультации. Согласно ему имеем
по теореме косинусов
По теореме синусов
-- искомая величина угла.
Можно, однако, получить значение косинуса искомого угла в радикалах и по нему вычислить искомую величину угла. Для этого воспользуемся тем, что по теореме синусов
а по теореме косинусов
тогда
то есть
или
но последнее решение не подходит, потому что угол
должен быть тупым.Итак,
Литература
Погорелов А. В. Геометрия. Учебник для 7 -- 11 классов общеобразовательных учреждений. -- М.: Просвещение, 1995. -- 383 с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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