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Консультация № 183350
25.05.2011, 16:12
50.59 руб.
0
4
2
Здравствуйте! У меня возникли сложности с таким вопросом:
1)Основанием прямоугольного параллелепипеда служит квадрат диагональ параллелепипеда равна 2[$8730$]6 см,а его измерения относятся как 1:1:2.Найти а)измерения параллелепипеда ; б)синус угла между диагональю параллелепипеда и плоскостью его основания.
2)Сторона квадрата ABCD равна a.Через сторону AD проведена плоскость альфа на расстоянии a/2 от точки B. Найти расстояние от точки C до плоскости альфа.б)Показать на рисунке линейный угол двугранного угла BADM, M принадлежит альфе.
1)Основанием прямоугольного параллелепипеда служит квадрат диагональ параллелепипеда равна 2[$8730$]6 см,а его измерения относятся как 1:1:2.Найти а)измерения параллелепипеда ; б)синус угла между диагональю параллелепипеда и плоскостью его основания.
2)Сторона квадрата ABCD равна a.Через сторону AD проведена плоскость альфа на расстоянии a/2 от точки B. Найти расстояние от точки C до плоскости альфа.б)Показать на рисунке линейный угол двугранного угла BADM, M принадлежит альфе.
Обсуждение
25.05.2011, 16:47
общий
это ответ
Здравствуйте, Посетитель - 366386!
1) Пусть сторона квадрата равна a. Так как измерения параллелепипеда относятся как 1:1:2, то его высота равна 2a. По трехмерной теореме Пифагора диагональ параллелепипеда равна
[$8730$](a2+a2+(2a)2=a[$8730$]6.
Диагональ параллелепипеда проектируется на основание в диагональ квадрата, поэтому тангенс искомого угла равен отношению высоты к диагонали квадрата:
tg[$966$]=2a/a[$8730$]2=[$8730$]2
sin[$966$]=tg[$966$]/[$8730$](1+tg2)[$966$]=[$8730$](2/3)
1) Пусть сторона квадрата равна a. Так как измерения параллелепипеда относятся как 1:1:2, то его высота равна 2a. По трехмерной теореме Пифагора диагональ параллелепипеда равна
[$8730$](a2+a2+(2a)2=a[$8730$]6.
Диагональ параллелепипеда проектируется на основание в диагональ квадрата, поэтому тангенс искомого угла равен отношению высоты к диагонали квадрата:
tg[$966$]=2a/a[$8730$]2=[$8730$]2
sin[$966$]=tg[$966$]/[$8730$](1+tg2)[$966$]=[$8730$](2/3)
Неизвестный
25.05.2011, 16:59
общий
1. По свойству прямоугольного параллелепипеда а2+b2+c2=d2
x2+x2+(2x)2=(2[$8730$]6)2
6x2=24
x=2
Итак измерения параллелепипеда 2, 2, 4
sina=4/2[$8730$]6=2/[$8730$]6
x2+x2+(2x)2=(2[$8730$]6)2
6x2=24
x=2
Итак измерения параллелепипеда 2, 2, 4
sina=4/2[$8730$]6=2/[$8730$]6
Форма ответа
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