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Консультация № 187723
27.01.2014, 20:44
79.10 руб.
0
2
2
Здравствуйте! Прошу помощи в следующем вопросе: Стороны треугольника равны 15, 37 и 44 см. Из вершины большего угла треугольника восстановлен к его плоскости перпендикуляр, равный 16 см. Найти расстояние от его концов до большей стороны. Заранее благодарен.
Обсуждение
27.01.2014, 23:00
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Стороны треугольника a=15,b=37,c=44
Вычисляем полупериметр p=0.5(15+37+44)=48
По формуле Герона вычисляем площадь
S=[$8730$]p(p-a)(p-b)(p-c)=264
Против большей стороны лежит больший угол, высота треугольника из этого угла
h=2S/c=12 (это расстояние от нижнего конца)
Отрезок, проведенный из вершины перпендикуляра к стороне c перпендикулярен этой стороне
(по теореме о трех перпендикулярах), поэтому его длина и есть расстояние до стороны.
Сам перпендикуляр, высота треугольника к стороне c и сторона c образуют прямоугольный треугольник,
поэтому второе рассточние находим по теореме Пифагора
[$8730$](162+122)=20
Ответ: 12 и 20
Стороны треугольника a=15,b=37,c=44
Вычисляем полупериметр p=0.5(15+37+44)=48
По формуле Герона вычисляем площадь
S=[$8730$]p(p-a)(p-b)(p-c)=264
Против большей стороны лежит больший угол, высота треугольника из этого угла
h=2S/c=12 (это расстояние от нижнего конца)
Отрезок, проведенный из вершины перпендикуляра к стороне c перпендикулярен этой стороне
(по теореме о трех перпендикулярах), поэтому его длина и есть расстояние до стороны.
Сам перпендикуляр, высота треугольника к стороне c и сторона c образуют прямоугольный треугольник,
поэтому второе рассточние находим по теореме Пифагора
[$8730$](162+122)=20
Ответ: 12 и 20
5
28.01.2014, 01:33
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Т.к. все интересующие нас треугольники - прямоугольные, то, применяя для них теорему Пифагора, получим еще один вариант решения:
Т.к. все интересующие нас треугольники - прямоугольные, то, применяя для них теорему Пифагора, получим еще один вариант решения:
Прикрепленные файлы:
5
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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