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Консультация № 142482
28.08.2008, 10:41
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Здравствуйте уважаемые эксперты.Вот такая вот задачка: Вы смотрите из окна на дерево находящееся на улице ,необходимо определить его высоту , не спускаясь на улицу.
Обсуждение
31.08.2008, 20:12
общий
это ответ
Здравствуйте, Боровков максим сергеевич!
Предложенная Вами задача решается с применением зависимостей, известных из школьного курса геометрии для прямоугольных треугольников.
Необходимо знать расстояние до дерева (обозначим его через L) и высоту, на которой расположено окно (обозначим его через H). Если измерить угломерным инструментом угол АЛЬФА, составленный горизонталью и направлением на верхушку дерева, то искомая высота дерева
h = H + L*tg АЛЬФА (если верхушка дерева находится выше окна),
h = H - L*tg АЛЬФА (если верхушка дерева находится ниже окна).
В случае, если расстояние L заведомо неизвестно, то необходимо выбрать и измерить какой-либо отрезок AB, расположенный на горизонтали, мысленно проведенной от окна к дереву и аналогично указанному выше измерить углы (обозначим их через АЛЬФА и БЕТА) в концах отрезка. Тогда
h = H + |AB| / (ctg БЕТА - ctg АЛЬФА) или h = H - |AB| / (ctg БЕТА - ctg АЛЬФА), в зависимости от взаимного расположения верхушки дерева и окна.
(Для определенности пусть угол БЕТА соотвествует точке B, а угол АЛЬФА - точке A, и пусть точка B находится ближе к дереву, чем точка A.)
С уважением.
Предложенная Вами задача решается с применением зависимостей, известных из школьного курса геометрии для прямоугольных треугольников.
Необходимо знать расстояние до дерева (обозначим его через L) и высоту, на которой расположено окно (обозначим его через H). Если измерить угломерным инструментом угол АЛЬФА, составленный горизонталью и направлением на верхушку дерева, то искомая высота дерева
h = H + L*tg АЛЬФА (если верхушка дерева находится выше окна),
h = H - L*tg АЛЬФА (если верхушка дерева находится ниже окна).
В случае, если расстояние L заведомо неизвестно, то необходимо выбрать и измерить какой-либо отрезок AB, расположенный на горизонтали, мысленно проведенной от окна к дереву и аналогично указанному выше измерить углы (обозначим их через АЛЬФА и БЕТА) в концах отрезка. Тогда
h = H + |AB| / (ctg БЕТА - ctg АЛЬФА) или h = H - |AB| / (ctg БЕТА - ctg АЛЬФА), в зависимости от взаимного расположения верхушки дерева и окна.
(Для определенности пусть угол БЕТА соотвествует точке B, а угол АЛЬФА - точке A, и пусть точка B находится ближе к дереву, чем точка A.)
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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