In an isosceles triangle, one external angle is 60, and the height to the side is 14. Calculate the length of the base of the triangle.

If the triangle is isosceles, then its angles at the base are equal.
The outer corner anyway belongs to the inner corner between the sides, because adjacent to it will be 120 °, and the angles at the base both cannot be 120 ° (the sum of the angles in the triangle is 180).
If the external angle is equal to the sum of two internal non-adjacent to it, and these two angles are equal to each other, then: 60 °: 2 = 30 °. (angles BAC and BCA 30 °)
If the height is drawn to the side of the aircraft (for example, AM), then the angle AMC = 90 °.
The AMC triangle is rectangular.
AM is a leg that lies opposite an angle of 30 degrees. By property, it is equal to half the hypotenuse. Hypotenuse AC. It will be 14 × 2 = 28cm.