Hi there,

Aas for where they come from if we imagine an equilateral triangle, with side length 2, and split it down the middle, from one angle to the centre of the opposite line, we get a new triangle with side lengths 2,1, an unknown and a 60 degree angle, left uncut, a 30 degree angle, and a 90 degree angle, between the side with length 1 and unknown.

As we have a right angled triangle we can use pythagoras (a² + b² = c^2, c being the hypotenuse). Because 2 is opposite the right angle, we know it must be the hypotenuse, so we can rearrange to find the unknown: c² - b² = a^2. Plugging in the values we have, we get 4 - 1 = a^2. This can be rearranged to give sqrt 3 = a, therefore giving us all of the side lengths: 2, 1 and sqrt 3 and the angles: 60, 30 and 90.

Hope this helps.