Height of Isosceles Triangle ABC

In triangle ABC, the lengths of sides AB and AC are equal, making it an isosceles triangle. Let the length of sides AB and AC be represented as $x$ units.

The angle at vertex A measures 40 degrees. If the length of base BC is 12 units, determine the height from vertex A to side BC, denoted as $h$. Use the properties of an isosceles triangle for your calculations.