Make a triangle (1) between the sailboat, the island and the rescue boat, a triangle (2) between the sailboat the island and the helicopter, a triangle (3) from the island to the helicopter by horizontal, vertical and direct distance and a similar triangle (4) from the sailboat to the helicopter.

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Make a triangle (1) between the sailboat, the island and the rescue boat, a triangle (2) between the sailboat the island and the helicopter, a triangle (3) from the island to the helicopter by horizontal, vertical and direct distance and a similar triangle (4) from the sailboat to the helicopter.

**Triangle (1)**

The angle between the island and the sailboat from the point of view of the rescue boat is A=35 and the angle between the resuce boat and the sailboat from the point of view of the island is B = 68. The third angle (the angle between the island and the rescue boat from the point of view of the sailboat) is then

C = 180 - (35+68) = 213`^@`

The distance ` `between the rescue boat and the sailboat is 800m. Using the sine rule, the distance `d` between the island satisfies

`sinB/800 = sinA/d`

Therefore `d = 800(sinA)/sinB = 800(sin35)/sin68 = 494.90m`

**Triangle (2)**

The angle between the sailboat and the island from the point of view of the helicopter is 40. and the distance between them is `d`. Call the other two angles ` `E and F. and the other two lengths `e` and `f` where `f` is the horizontal distance between the island and the helicopter.

Now `sin40/800 = sinE/e = sinF/f`

So `e = f((sinE)/sinF)` and `E + F = 180-40 = 140`

**Triangle (3)**

The elevation of the helicopter is 73 from the point of view of the island. The vertical height `g` of the helicopter satisfies

`(sin73/g) = sin(90-73)/f`

`implies g = f(sin73)/sin(17) = 0.704f`

**Triangle (4)**

We now have that the direct distance `h` between the helicopter and the sailboat satisfies

`h^2 = e^2 +g^2 = f^2(0.704^2 + ((sinE)/(sinF))^2)`