In an isosceles triangle, 1 of the outer corners = 60 degrees. Height drawn to the side = 5cm. Find the base.

The outer corner CBD is adjacent to the inner corner ABC of the triangle ABC. Since the sum of adjacent angles is 180, the angle ABC = (180 – CBD) = (180 – 60) = 120.

The ABC triangle is isosceles, then the angle BAC = BCA = (180 – ABC) / 2 = (180 – 120) / 2 = 30.

The ADC triangle is rectangular, since CD is the height of the ABC triangle, then the CD leg is located opposite the angle 30, and therefore, it is half the length of the AC hypotenuse.

Then AC = CD * 2 = 5 * 2 = 10 cm.

Answer: The length of the base of the speaker is 10 cm.