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сума двох сторін трикутника, між якими кут 60 градусів, дорівнює 11 см, а їхня третя сторона - 7 см, знайдіть невідомі сторони!!!!!!!!
срочно
даю 8 балов
Ответы 1
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Нехай ВС=х, тоді за умовою АВ=11-х, АС=7 см.∠В=60°. соs60=0,5.Застосуємо теорему косинусів.АС²=ВС²+АВ²-2·ВС·АС·соs В;49=х²+(11-х)²-2·х·(11-х)·0,5;49=х²+121-22х+х²-11х+х²;3х²-33х+72=0,скорочуємо на 3,х²-11х+24=0, за теоремою Вієта маємо корені х1=3; х2=8ВС=3 см; АВ=11-3=8 см.
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Автор:
jaliyah - 5 лет назад
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