(Just copy and paste the links below)

Call the height of the helicopter, h

And call the distance that Amanda is from a point directly below the helicopter , x

So....the distance that Jeremiah is from this point is  4000 - x

So  we have that

tan (60)  =  h / x   ⇒   x tan (60)  = h       (1)

and

tan (30)  =  h / ( 4000 - x)  ⇒    tan(30) (4000 - x)  =  h      (2)

Equating  (1)  and (2), we have that

x tan (60)  =  (4000 - x) tan (30)   simplify

xsqrt (3)  =  (4000- x)  (1/ sqrt (3) )          multiply both sides by  sqrt 930

3x  =  4000 - x      add x to both sides

4x  = 4000   divide both sides by 4

x  = 1000

So...Amanda's distance from the helicopter is      cos (60)  =   1000/ Amanda's distance to helicopter  =

1000/ cos (60)  = Amanda' s distance to the helicopter = 1000/(1/2)  =  2000 ft 

Jeremiah's distance to the helicopter is

cos (30)  =  ( 4000 - x )  / Jeremiah's distance to the helicopter

cos (30)  =  3000 /  Jeremiah's distance to the helicopter

Jeremiah's distance to the helicopter   =   1000/ cos (30)  ≈  3464 ft 

3.  The height of the helicopter  is  1000 tan (60)  ≈  1732 ft

4. Jeremiah  is  (4000 - 1000)   = 3000 ft from the rope

5. Amanda is 1000 ft from the rope