Question

Две стороны треугольника равны 33 и 37 а угол противолежащий большей из них 120 найти периметр и площадь

Answer 1

задача довольно тупая, смысл решения такой - по теореме косинусов находим третью сторону, потом по формуле Герона считаем площадь.

a^2 + 33^2 - 2*a*33*cos(120) = 37^2;

a^2 + 33*a +33^2 - 37^2 = 0;

a = -33/2 + корень(33^2 + 4*280)/2 = (47 - 33)/2 = 7;

Периметр равен 33 + 37 + 7 = 77;

полупериметр р = 77/2, р - 37 = 3/2; p - 33 = 11/2; p - 7 = 63/2;

S^2 = 77*63*11*3/16 = (7*11*3/4)^2*3;

S = 231*корень(3)/4;

Answer 2

Given Information

We are given that two sides of a triangle are equal to 33 and 37, and the angle opposite the larger side is 120 degrees.

Solution

To find the perimeter and area of the triangle, we can use the Law of Cosines to find the length of the third side, and then apply the formulas for perimeter and area.

Finding the Length of the Third Side

The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we have two sides of the triangle equal to 33 and