In an isosceles triangle PQS, the angle Q is 120, the lateral side is 10 inches. The height PH was drawn from the vertex P.

In an isosceles triangle PQS, the angle Q is 120, the lateral side is 10 inches. The height PH was drawn from the vertex P. Find the length of the line segment HS.

So, after building the height, we see that two right-angled triangles are formed, equal to each other. Since the 120-degree angle is halved, there are two 60-degree angles, and the other acute angles are 30 degrees. Therefore, HS is equal to one half of the hypotenuse, and, accordingly, HS is 5 dm.