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Консультация № 146517
08.10.2008, 21:38
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Здравствуйте уважаемые эксперты!Прошу помочь в решении задачи-7.
Угол при вершине равнобедренного треугольника равен 56°. На его боковой стороне, как на диаметре, построена полуокружность, которая основанием треугольника разделилась на две части. Найдите эти части.
Угол при вершине равнобедренного треугольника равен 56°. На его боковой стороне, как на диаметре, построена полуокружность, которая основанием треугольника разделилась на две части. Найдите эти части.
Обсуждение
Неизвестный
08.10.2008, 22:15
общий
это ответ
Здравствуйте, Бортников Артём Михайлович!
Пусть вершина будет в точке В, а две другие вершины А и С
пусть полуокружность построена на стороне АВ, тогда d=AB, r=AB/2;
пусть эта полуокружность пересекает сторону AC в точке D, тогда AD=r=AB/2
нам надо найти отношение DC/AD=(AC-AD)/AD=AC/AD - 1=AC/ (AB/2) -1 =2*AC/AB -1
DC/AD=2*AC/AB -1 (*)
найдем соотношения между AC и AB
для начала найдем остальные 2 угла, они равны (180°-56°)/2=62°
теперь воспользуемся теоремой синусов:
AC/sinB = AB/sinC
AC/AB= sinB/sinC=sin56°/sin62° подставим это в (*):
DC/AD=2*sin56°/sin62° -1 = 0.878
Пусть вершина будет в точке В, а две другие вершины А и С
пусть полуокружность построена на стороне АВ, тогда d=AB, r=AB/2;
пусть эта полуокружность пересекает сторону AC в точке D, тогда AD=r=AB/2
нам надо найти отношение DC/AD=(AC-AD)/AD=AC/AD - 1=AC/ (AB/2) -1 =2*AC/AB -1
DC/AD=2*AC/AB -1 (*)
найдем соотношения между AC и AB
для начала найдем остальные 2 угла, они равны (180°-56°)/2=62°
теперь воспользуемся теоремой синусов:
AC/sinB = AB/sinC
AC/AB= sinB/sinC=sin56°/sin62° подставим это в (*):
DC/AD=2*sin56°/sin62° -1 = 0.878
Форма ответа
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