Usually when you need to calculate trigonometry values such as sin15 and cos15 then you can use: However, I found an alternative method using geometry directly.
Firstly you draw an isosceles triangle ABC (A is the top angle) with A = 30, B=C = 75. Now draw a line from B that is perpendicular to AC at a point D. This means that ABD = 60 and DBC = 15 BCD = 75. Also, without loss of generality, let AB = 2
By using special triangle AB = 2, BD = 1 and AD = DC = 2 - . Now by using pythagoras' theorem: So now we have a rightangle triangle BCD where all the sides are known.