20 minutes after being launched, a hot-air balloon has risen to an altitude of 300m. the pilot can still see the starting pt on the ground at a 25 degree angle of depression. how many meters is the balloon from the starting pt?
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assuming you mean line-of-sight distance,
300/x = sin 25°
If you mean how far long the ground has he traveled, then
300/x = tan 25°
To find the distance between the balloon and the starting point, we can use trigonometry and the angle of depression.
First, let's draw a diagram to visualize the situation. We have a right triangle where the height of the balloon is the vertical side, and the distance between the balloon and the starting point is the hypotenuse.
```
|
| /
| / height (300m)
25° | /
| /
Starting point |-------
```
In this diagram, the angle of depression is 25 degrees, and the height of the balloon is 300m.
Now, let's use the tangent function, which relates the angle of depression to the ratio of the height and the distance.
tan(angle) = height / distance
Plugging in the values we know:
tan(25°) = 300m / distance
To isolate the distance, we rearrange the equation:
distance = height / tan(angle)
Calculating the distance:
distance = 300m / tan(25°)
≈ 687.6m
Therefore, the balloon is approximately 687.6 meters from the starting point.