To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. [Graphs generated by this script: setBorder(0); initPicture(-5,5,-3,4); text([0,-2.5], "3.76 km"); text([-2,1], "2.47 km"); text([-4.3,-2.3], "C"); text([1,3.3], "B"); text([4.3,-2.3], "A"); text([-2.7,-1.5],"37.7°"); stroke = "blue"; strokewidth = "5"; path([[4,-1.8],[3,-1.5],[2,-1.7],[1,-1.8],[0,-1.5],[-0.4,-1],[-0.6,0],[0,1],[1,1.4],[1.1,2.5],[1.3,2.9],[2,2.7],[3,2.2],[3.3,2],[4,1],[4.6,0],[4.7,-0.3],[4.6,-1],[4,-1.8]]); strokewidth = "2"; stroke = "red"; path([[1,3],[-4,-2],[4,-2]]); strokedasharray = "7,3"; line([1,3],[4,-2]); strokedasharray = "1,0"; stroke = "black"; strokewidth = "1"; arc([-3.3,-2],[-3.505,-1.505],.7); ] NOTE: The triangle is NOT drawn to scale.

distance = km

Enter your answer as a number; your answer should be accurate to 2 decimal places.