Answer
The distance between the rescue and life boat is $= 2130.1$ ft.
Work Step by Step
1. Find the angle inside the small $\triangle$
$= 90 - 28$
$= 62^{\circ}$
2.Use the tangent ratio to find the horizontal distance between the helicopter and lifeboat if they were both on the same altitude
Let $x =$ distance
$tan(62) = \frac{x}{1000}$
$x = 1000tan(62)$
by GDC / calculator
$x = 1880.726465$ ft
3. Find the angle inside the large $\triangle$
$= 90 - 14$
$= 76^{\circ}$
4. Use the tangent ratio to find the horizontal distance between the helicopter and the rescue boat if they were both on the same altitude Let $a = $ distance
$tan(76) = \frac{a}{1000}$
by GDC / calculator
$a = 4010.780934$ ft
5. Subtract the larger distance from the smaller distance to find the distance between the life boat and the rescue boat
Let $d = $ distance
$d = (4010.78...) - (1880.726...)$
$d = 2130.054469$ ft
$d= 2130.1$ ft