In an isosceles triangle, the side is 10 and the angle opposite the base is 120. Find the area of the triangle.

Since the triangle is isosceles, its angles at the base are equal. The angle B, at the top, is equal to 1200 by condition, then the angles at the base will be equal to (180 – 120) / 2 = 30.

Let us omit the height of the ВD from the apex and consider the right-angled triangle of the AВD. The height of the ВD lies opposite an angle of 30, therefore, it is equal to half of the hypotenuse AB. ВD = AB / 2 = 10/2 = 5 cm.

Then the area of the triangle ABC is S = (AB * ВD) / 2 = 10 * 5/2 = 25 cm2.

Answer: S = 25 cm2.