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Консультация № 144223
17.09.2008, 19:58
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Каждый из углов, прилегающих к одной из сторон треугольника, равен α, радиус окружности, описанной около треугольника, равен R. Найти периметр треугольника.
Приложение:
решите пожалста поскорее
Приложение:
решите пожалста поскорее
Обсуждение
17.09.2008, 22:35
общий
это ответ
Здравствуйте, Belmont!
Пусть дан треугольник ABC, в котором [$8736$]A = [$8736$]B. Тогда, используя общепринятые обозначения, по расширенной теореме синусов имеем
a / sin [$8736$]A = b / sin [$8736$]B = c / sin [$8736$]C = 2[$149$]R. Пусть, согласно условию, [$8736$]A = [$8736$]B. Тогда треугольник ABC - равнобедренный, и
a = b, [$8736$]C = 180[$186$] - 2[$149$][$8736$]A, c / sin [$8736$]C = c / sin (180[$186$] - 2[$149$][$8736$]A) = c / sin 2[$149$][$8736$]A.
Тогда периметр треугольника
P = a + b + c = 2[$149$]R[$149$](sin [$8736$]A + sin [$8736$]A + sin 2[$149$][$8736$]A) = 4[$149$]R[$149$]sin [$8736$]A[$149$](1 + cos [$8736$]A) =
= 4[$149$]R[$149$]sin [$945$][$149$](1 + cos [$945$]).
С уважением.
Пусть дан треугольник ABC, в котором [$8736$]A = [$8736$]B. Тогда, используя общепринятые обозначения, по расширенной теореме синусов имеем
a / sin [$8736$]A = b / sin [$8736$]B = c / sin [$8736$]C = 2[$149$]R. Пусть, согласно условию, [$8736$]A = [$8736$]B. Тогда треугольник ABC - равнобедренный, и
a = b, [$8736$]C = 180[$186$] - 2[$149$][$8736$]A, c / sin [$8736$]C = c / sin (180[$186$] - 2[$149$][$8736$]A) = c / sin 2[$149$][$8736$]A.
Тогда периметр треугольника
P = a + b + c = 2[$149$]R[$149$](sin [$8736$]A + sin [$8736$]A + sin 2[$149$][$8736$]A) = 4[$149$]R[$149$]sin [$8736$]A[$149$](1 + cos [$8736$]A) =
= 4[$149$]R[$149$]sin [$945$][$149$](1 + cos [$945$]).
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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