To find the distance across a river, a surveyor choose points A and B, which are 247 ft apart on one side of the river. She then chooses a reference point C on the opposite side of the river and finds that $\displaystyle \angle{B}{A}{C}\approx{86}°$ and $\displaystyle \angle{A}{B}{C}\approx{58}°$. [Graphs generated by this script: setBorder(0); initPicture(0,6,0,4); text([3.6,2.8],"58°"); text([2.6,2.6],"86°"); text([3.25,3.7],"247 ft"); text([4.5,3.7],"B"); text([2,3.7],"A"); text([2.5,0.3],"C"); stroke="blue"; strokewidth="6"; line([0,3.2],[6,3.2]); line([0,0.8],[6,0.8]); strokewidth="1"; stroke="red"; strokewidth="2"; path([[2,3.4],[4.5,3.4],[2.5,0.6],[2,3.4]]); stroke = "black"; strokewidth = "1"; arc([2.105,2.809],[2.6,3.4],.6); arc([3.9,3.4],[4.151,2.912],.6); ] NOTE: The picture is NOT drawn to scale.

Approximate the distance from point A to point C.
distance = ft
Find the distance across the river.
height = ft

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