Working out trig without a calculator?

[flibbage0]

I know this might sound really stupid and easy but how do I work out Sin 60 without using a calculator?

Is it just Sin (45+15) and then I'm supposed to know what Sin 45 and Sin 15 are?

Thanks.

 

[flibbage0]

Sine is the ratio of opp to hyp. So if you take a 30-60-90 triangle you can see sin(60)=½√3

How do I do that, so I have a triangle with 3 angles but don't know what any of the side lengths are

 

[flibbage0]

if you take an equilateral triangle with sides 2-2-2 and split it in half you get a 30-60-90 triangle. Obviously you know one side is 1 and another is 2. You can use pythagoras to find the other is √3

I see, thank you very much

So I am supposed to remember that then.