1.найти неизвестную сторону треугольника-mnp, mn=3см; np=7см; угол m=120 градусов. 2.в параллелограмме острый угол=60 градусам, стороны 6 и 2см. найти длину большой диагонали.

Треугольник мнр, мн=3, нр=7, уголм=120, нр в квадрате=мр в квадрате+мн в квадрате-2*мр*мн*cos120, 49=мр в квадрате+9-2*мр*3*(-1/2), мр в квадрате-3мр-40=0, мр=(-3+-корень(9+4*40))/2=(3+-13)/2, мр=8,    параллелограмм авсд, ав=2, вс=6, угола=60, уголв=120, ас-большая диагональ, ас в квадрате=ав в квадрате+вс в квадрате-2*ав*вс*cos120=4+36-2*2*6*(-1/2)=52, ас=2*корень13

Объяснение:

Обозначим величину угла ACB через х.

Выразим через х величину угла ВАС.

Согласно условию задачи, величина угол BAC в 2 раза больше, чем величина угла ACB, следовательно, величина угла ВАС составляет 2х.

Рассмотрим треугольник АВС.

В данном треугольнике угол АВС является прямым.

Поскольку сумма углов любого треугольник равна 180°, можем составить следующее уравнение:

х + 2х + 90 = 180.

Решаем полученное уравнение и находим величину угла ACB:

3х + 90 = 180;

3х = 180 - 90;

3х = 90;

х = 90 / 3;

х = 30°.

Находим величину угла ВАС:

2х = 2 * 30 = 60°.

ответ: угол ACB равен 30°, угол BAC равен 60°.

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