Which trigonometric equation correctly models the distance the swimmer swam toward the buoy in terms of x and y ?

Question

A rescue team is deployed via helicopter to rescue a struggling swimmer. The helicopter locates the swimmer, who is several feet from a tethered buoy. The helicopter hovers 400 feet over the buoy as its team prepares to rescue the swimmer. Initially, the swimmer sees the helicopter at an angle of elevation of x degrees. The swimmer then swims 5 feet closer to the buoy, and now sees the helicopter at an angle of y degrees.

Answer 1

Draw a figure!  Assume the line from the head of the swimmer to the top of the buoy is ⊥ to the line from the buoy to the helicopter.  Let d = the original distance from the swimmer to the buoy, then d-5 is the distance after the swimmer moved closer.

 

Then tan x = 400/d and tan y = 400((d-y);

d tan x = (d-5) tan y = 400

This might be simplified a little, but I think it should suffice for your answer.