Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than $\displaystyle \angle{C}{A}{B}={42.6}°$. Find the distance across the lake from A to B. [Graphs generated by this script: setBorder(0); initPicture(-5,5,-3,4); text([0,-2.5], "354 ft"); text([-2,1], "486 ft"); text([-4.3,-2.3], "C"); text([1,3.3], "B"); text([4.3,-2.3], "A"); text([2.7,-1.2],"42.6°"); 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([3.588,-1.314],[3.2,-2],.8); ] NOTE: The triangle is NOT drawn to scale.

distance = ft

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