Вопрос школьника по предмету Геометрия
В прямоугольном треугольнике один из углов равен 60°, радиус описанной в него окружности равен 4 см. Найдите площадь треугольника.
Ответ учителя по предмету Геометрия
R=4см⇒c=2R=8см-гипотенуза
<B=60⇒<A=90-60=30⇒a=1/2*c=4см
b=√(c²-a²)=√(64-16)=√48=4√3см
S=1/2*ab=1/2*4*4√3=8√3см²
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