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Консультация № 145993
04.10.2008, 18:12
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Уважаемые эксперты!Помогите,пожалуйсто,с задачей.Заранее спасибо.
Дан квадрат ABCD со стороной, равной 1 см. Точка K принадлежит стороне CD и отрезки СК и KD относятся, как 1:2. Найти расстояние от вершины C до прямой АК.
Дан квадрат ABCD со стороной, равной 1 см. Точка K принадлежит стороне CD и отрезки СК и KD относятся, как 1:2. Найти расстояние от вершины C до прямой АК.
Обсуждение
Неизвестный
05.10.2008, 14:17
общий
это ответ
Здравствуйте, Screed!
Пусть СО – расстояние от вершины С до прямой AK.
Тогда рассмотрим треугольники СОК и AKD. Они подобны по трем углам.
Тогда СО/AD =СК/AK. Следовательно СО = СК * AD / АК.
СК = 1/3. AD = 1.
АК найдем из прямоугольного треугольника AKD:
(AK)^2 = (AD)^2 + (KD)^2 , где АD = 1 и KD = 2/3.
Произведя все вычисления получим AK = √13 / 3.
Следовательно СО = 1/√13 ≈ 0,29
Пусть СО – расстояние от вершины С до прямой AK.
Тогда рассмотрим треугольники СОК и AKD. Они подобны по трем углам.
Тогда СО/AD =СК/AK. Следовательно СО = СК * AD / АК.
СК = 1/3. AD = 1.
АК найдем из прямоугольного треугольника AKD:
(AK)^2 = (AD)^2 + (KD)^2 , где АD = 1 и KD = 2/3.
Произведя все вычисления получим AK = √13 / 3.
Следовательно СО = 1/√13 ≈ 0,29
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