The sides of all 30-60-90 triangles are in the proportion , where is the hypotenuse of the triangle and is the side directly opposite to the 30 degree angle.
Since the base of the triangle is directly opposite to the 30 degree angle, the hypotenuse, j, must be equal to
You could roll a 6-sided die 3 times to simulate this. This is a good simulation because it has one side for each possible tool, and each roll is independent, just as selecting the tool with replacement would be.
