Picture the triangle you described. Now picture a vertical line drawn from the peak down to the middle of the base. This represents the altitude, and note that since the triangle is isosceles (and therefore symmetric), this line splits the triangle perfectly in half, forming two congruent right triangles (identical but mirror images of each other). These are both right triangles whose hypotenuses are formed by the two sides of length 10mm. One leg of each right triangle is formed by half the base of the original triangle, so each has a length of 6mm. The remaining leg of each triangle is formed by the line you drew to represent the altitude, and it's length is unknown. To find it, simply use the Pythagorean theorem:



Just solve for h.