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Question

Hello! I was wondering about this math problem, because our teacher never went over this with us! Here it is: A sailor spots a whale through her binoculars. She wonders how far away the whale is, but the whale does not show up on the radar system. She sees another boat in the distance and radios the captain asking him to spot the whale and record its direction. Explain how this added information could enable the sailor to pinpoint the location of the whale. Under what circumstance would this idea fail?

Answer 1

A is the location of the first boat.

B is the location of the second boat.

W is the location of the whale.

 

Nothing is said about A seeing B on radar, so assume it shows up. Distance AB is known.

Nothing is said about B seeing W on radar, so assume it shows up.

m∠WBA can be determined.

 

Using Law of Sines, AW can be determined.

 

 

Answer 2

If the captain of the other vessel spots the whale (so, this fails if he can't spot it or record its angle or distance [also out of his radar range]) and reports the angle and distance from his boat, then transforming that angle and distance into the angle and distance from the sailor's boat is just a matter of trigonometry conversions (note: this is like axis transformation).
 
This calculation also fails if the sailor cannot determine both the distance from her boat to the other boat (the other boat must be on her radar) and the angle (as she sees it) between the whale and the other boat