An airplane pilot over the Pacific sights an atoll at an angle of depression of 7°. At this time, the horizontal distance from the airplane to the atoll is 3,729 meters

What is the height of the plane to the nearest meter?

1 answer

We can use trigonometry to solve this problem. Let's draw a diagram:

```
Pilot
/|
/ | height (h)
/ |
-------
Atoll d = 3729 meters
```

The angle of depression is the angle between the horizontal and the line of sight from the pilot to the atoll. Let's call this angle `A`. Then:

```
tan(A) = opposite / adjacent
```

In this case, the opposite is the height of the plane, `h`, and the adjacent is the horizontal distance, `d`. So we get:

```
tan(7°) = h / 3729
h = 3729 * tan(7°)
h ≈ 454 meters
```

So the height of the plane, to the nearest meter, is 454 meters.