a lighthouse bears N 33 degrees E from a boat 6 miles from it. the boat sails west 8 miles. what is the distance of the lighthouse from the new position of the boat.
Draw a figure.
Place the boat B on an east-west line, 8 mi east of C
In triangle CBL, angle B = 123° and using the law of cosines, the distnce CL is
CL^2 = 8^2 + 6^2 - 2*8*6 cos123°