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Консультация № 198636
19.05.2020, 05:36
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Дан треугольник АВС, где АВ = 25 см, ВС = 56 см, АС = 39 см. Через сторону ВС проведена плоскость, образующая с плоскостью треугольника угол 600. Найти расстояние от точки А до плоскости.
Дан треугольник АВС, где АВ = 25 см, ВС = 56 см, АС = 39 см. Через сторону ВС проведена плоскость, образующая с плоскостью треугольника угол 600. Найти расстояние от точки А до плоскости.
Обсуждение
24.05.2020, 04:53
общий
это ответ
Здравствуйте, Трегубов Владислав Анатольевич!
Выберем на стороне BC точку D таким образом, что AD [$8869$] BC (то есть AD - высота). Тогда для прямоугольных треугольников ABD и ACD имеем соответственно
и
Второе равенство с учётом того, что BD + CD = BC и CD = BC - BD, принимает вид
или
Приравнивая правые части, получаем
откуда
В данном случае для AB = 25 см, ВС = 56 см, АС = 39 см
см,
откуда
см.
Теперь выберем на плоскости точку E таким образом, чтобы отрезок AE был перпендикулярен плоскости. Тогда треугольник ADE будет прямоугольным c гипотенузой AD и углом при вершине D, равным 60[$186$], и по свойству прямоугольного треугольника AE = AD sin A = 15[$183$]sin 60[$186$] = 15[$8730$]3/2 [$8776$] 13 см - искомое расстояние от точки А до плоскости.
Выберем на стороне BC точку D таким образом, что AD [$8869$] BC (то есть AD - высота). Тогда для прямоугольных треугольников ABD и ACD имеем соответственно
и
Второе равенство с учётом того, что BD + CD = BC и CD = BC - BD, принимает вид
или
Приравнивая правые части, получаем
откуда
В данном случае для AB = 25 см, ВС = 56 см, АС = 39 см
см,откуда
см.Теперь выберем на плоскости точку E таким образом, чтобы отрезок AE был перпендикулярен плоскости. Тогда треугольник ADE будет прямоугольным c гипотенузой AD и углом при вершине D, равным 60[$186$], и по свойству прямоугольного треугольника AE = AD sin A = 15[$183$]sin 60[$186$] = 15[$8730$]3/2 [$8776$] 13 см - искомое расстояние от точки А до плоскости.
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