Good shore points in NJ?

Precalculus Question: The bearings of two points on the shore from a boat are 115 degrees and 123 degrees.?

• The bearings of two points on the shore from a boat are 115 degrees and 123 degrees. Assume the two points are 855 feet apart. How far is the boat from the nearest point on shore if the shore is straight and runs north-south?

• Answer:

  let x = distance from shore, let y = distance north of line perpendicular to shore from first bearing point tan115 = x/y tan 123 = x/(y+855) so x = ytan(115) sub into the other equation tan(123) = x/(y+855) tan(123) = ytan(115)/(y+855) tan(123)(y+855) = ytan(115) ytan(123)+855tan(123) = ytan(115) 855tan(123) = ytan(115)-ytan(123) 855tan(123) = y(tan(115)-tan(123)) y = 855tan(123) / (tan(115)-tan(123)) y = 2177.5 x = 4669.6 feet west of shore