Question

a passenger on a cruise ship is positioned 42m above the water level and is admiring a tropical island in the distance. one end of the island is at a true bearing of 028 degrees and has an angle of depression of 11 degrees. while the other end is at a true bearing of 118 degrees and has an angle of depression of 19 degrees. how long is the island? Diagram required.

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Answer 1

Sure, I can help you with that! Here's a diagram to help visualize the problem:

```
A
/
/ 11°
/
/
28° /
/
/
/
/
B ____/________________ C
19° 118°
```

In this diagram, the passenger is at point A, 42 meters above the water level. The two ends of the island are represented by points B and C, and the angles of depression from these points are given in the diagram.

To find the length of the island, we can use trigonometry. Let x be the distance from the passenger to point B, and let y be the distance from the passenger to point C. Then:

```
tan(11°) = 42 / x => x = 42 / tan(11°) ≈ 222.5 m
tan(19°) = 42 / y => y = 42 / tan(19°) ≈ 125.7 m
```

So the length of the island, BC, is:

```
BC = x + y ≈ 348.2 m
```

I hope that helps! Let me know if you have any further questions.