math
posted by matt .
You have found a summer job manning a lighthouse off the northern coast of Vancouver Island. It is a lonely job and you feel the need for some mental stimulation. In your position, 40 m above sea level, you observe two sailboats in line with the lighthouse. The angles of depression to the two boats are 22 degrees and 67 degrees. You wish to determine how far apart the ships are.

if the near ship is at distance a,
the distance between the ships is b,
a/40 = cot67°
(a+b)/40 = cot22°
b = 40(cot22°cot67°) = 82.02