В треугольнике две стороны равня 12 и 8 см, а угол между ними 60 градусов .Найди...

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В треугольнике две стороны равня 12 и 8 см, а угол между ними 60 градусов .Найдите площадь треугольника

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Улиана

Имеем треугольник ABC. AB=12, BC=8. Проведем высоту АК. Угол ВАК=90-60=30. Тогда ВК=АВ/2=12/2=6. AK=sqrt(AB2-BK2)=sqrt(122-62)=sqrt(108)=6*sqrt(3).
SABC=BC*AK/2=8*6*sqrt(3)/2=24*sqrt(3)

Можно проще:
SABC=1/2*AB*BC*Sin60=1/2*12*8*sqrt(3)/2=24sqrt(3)

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