The area of an isosceles triangle is 196 √3. The angle opposite the base is 120 °. Find the length of the side.

As we know from the school mathematics course, in this type of triangles, the lengths of the sides are the same.

Let us express the length of the side, for which we will use the variable a.

Then, according to the well-known formula for calculating the area, the area of this triangle can be represented as a * a * sin 120 °: 2.

Since we know the area of our figure, then we can write down the equation and find out the length of the side:

a * a * sin 120 °: 2 = 196√3;

√3 / 4 * a ^ 2 = 196√3;

a ^ 2 = 784;

a1 = 28;

a2 = -28 (not suitable).

Answer: 28 cm.