Triangles ABC and DFG
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105° can be expressed as 60°+45°. What we have then is sin(60°+45°). The sum pattern for sin is sin(a)cos(b)+cos(a)sin(b). We will fill in as follows: sin(60)c0s(45)+cos(60)sin(45). Now draw those special right triangles in the first quadrant to get the exact values for each. The sin of 60 is 
, the cos of 45 is 
, the cos of 60 is 1/2, and the sin of 45 is . When we put all that together we get 
. Simplifying all of that we have 
. We can put that over the common denominator that is already there and get 
. Not sure if that's simplified enough; you may be at the point in class where you are rationalizing your denominator, but I'm not sure, and if you're not, I don't want to confuse you.