I have no idea why they placed the origin that way . . . very inconsiderate!
Listening post are at A, B, and C.
Point A is 2000ft north of point B, and point C is 2000ft east of B.
The sound of a gun reaches A and B simultaneously one second after it reaches C.
Show that the coordinates of a gun's position are approximately (1860,1000),
where the origin is at B. .Assume that sound travels 1100ft/sec
| * d+1100
2000 | *
| * G
| * * d+1100
| *d *
| * *
* - - - - - - - - - - - *
B 2000 C
The gun is at G(x,y).
Let GB = d. .Then GA = GC = d + 1100
Since G is equidistant from A and C, it lies on the 45°-line: x = y
The distance from G(x,x) to B(0,0) is: .√(2x²) .= .d
The distance from G(x,x) to C(2000,0) is: .√[(x - 2000)² + x²] .= .d + 1100
And we have this system of equations:
. . . . . . . . . . . 2x² .= .d²
. . (x - 2000)² + x² .= .(d + 1100)²