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Консультация № 201642
09.11.2021, 18:06
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Здравствуйте! У меня возникли сложности с таким вопросом:
[b]На катете AC прямоугольного треугольника ABC с прямым углом A выбраны точки D и E (D между A и E). Известно, что AD=1, DE=2, EC=3 и ?DBE=?ACB. Найдите длину отрезка AB.[/b]
[b]На катете AC прямоугольного треугольника ABC с прямым углом A выбраны точки D и E (D между A и E). Известно, что AD=1, DE=2, EC=3 и ?DBE=?ACB. Найдите длину отрезка AB.[/b]
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Обсуждение
10.11.2021, 06:27
общий
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Вы употребили красный цвет в тексте своего Вопроса. По неписанной традиции Портала только модераторам можно использовать красный цвет для внесения поправок (для исправления орфографических ошибок и прочих ляпов).
Я к своему стыду не могу вспомнить, какой республике стране/принадлежит Ваш флаг с красно-чёрно-зелёной раскраской? Я заглянул в Вашу Регистрационную карту в надежде увидеть Ваше "о Себе", но Вы не заполнили карту.
Откуда у Вас эта задача? Вероятно, с какой-то олимпиадной мат-фирмы типа ЗФТШ / Сириус ?
Я к своему стыду не могу вспомнить, какой республике стране/принадлежит Ваш флаг с красно-чёрно-зелёной раскраской? Я заглянул в Вашу Регистрационную карту в надежде увидеть Ваше "о Себе", но Вы не заполнили карту.
Откуда у Вас эта задача? Вероятно, с какой-то олимпиадной мат-фирмы типа ЗФТШ / Сириус ?
11.11.2021, 05:44
общий
11.11.2021, 11:36
это ответ
Условие: В прямоугольном треугольнике ABC : AD = 1, DE = 2, EC = 3 , [$8736$]DBE = [$8736$]ACB .
Вычислить длину катета AB.
Решение: Для удобства-краткости обозначим [$8736$]DBE = [$8736$]ACB = [$947$] , а [$8736$]ABD = [$966$] .
Легко заметить связь катетов: AB = AC·tg([$947$]) = (AD + DE + EC)·tg([$947$])
Аналогично связаны катеты AD = AB·tg([$966$]) , AE = AD+DE = AB·tg([$966$]+[$947$]) .
Решать эту систему уравнений Вы можете любым удобным Вам способом (в тч используя OnLine-решатели).
Я люблю вычислять в популярном приложении Маткад (ссылка) . Маткад избавляет меня от частых ошибок. Маткад-скриншот с оптимизированным рисунком прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ: AB = 3 ед. Проверка сделана.
Примечание: Поскольку в Условии не требуется вычисление углов, Вы можете упростить свою систему уравнений заменой:
tg([$947$]) = p , tg([$966$]) = q , tg([$947$] + [$946$]) = (p+q) / (1 - p·q) . =Удачи!
Вычислить длину катета AB.
Решение: Для удобства-краткости обозначим [$8736$]DBE = [$8736$]ACB = [$947$] , а [$8736$]ABD = [$966$] .
Легко заметить связь катетов: AB = AC·tg([$947$]) = (AD + DE + EC)·tg([$947$])
Аналогично связаны катеты AD = AB·tg([$966$]) , AE = AD+DE = AB·tg([$966$]+[$947$]) .
Решать эту систему уравнений Вы можете любым удобным Вам способом (в тч используя OnLine-решатели).
Я люблю вычислять в популярном приложении Маткад (ссылка) . Маткад избавляет меня от частых ошибок. Маткад-скриншот с оптимизированным рисунком прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ: AB = 3 ед. Проверка сделана.
Примечание: Поскольку в Условии не требуется вычисление углов, Вы можете упростить свою систему уравнений заменой:
tg([$947$]) = p , tg([$966$]) = q , tg([$947$] + [$946$]) = (p+q) / (1 - p·q) . =Удачи!
5
11.11.2021, 17:16
общий
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Огромное спасибо вам большое за помощь. Хорошо, я извиняюсь за использование красного цвета, я не знал о этом. Флаг же принадлежит государству Ливия. Задача же с сириуса.
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