In a triangle, one of the sides is 8, the other is 7√3, and the angle between them is 120 degrees.

In a triangle, one of the sides is 8, the other is 7√3, and the angle between them is 120 degrees. Find the area of this triangle.

As we know from the school geometry curriculum, in order to calculate the area of such a geometric figure, it is possible to use the following formula:

S = 1/2 * a * b * sin a, where sin a is the sine of the angle that will be between the multiplied sides.

Let us determine what value the area of this triangle will equal if from the condition of our problem we know for sure that between the sides at 8 and 7√3 there is an angle equal to 120 °:

sin 120 ° = √3 / 2;

1/2 * 8 * 7√3 * √3 / 2 = 2 * 7 * 3 = 42.

Answer: 42.