Advanced Mathematical Concepts: Precalculus with Applications. Glencoe. 2006.
It asks students to ignore reality in order to solve it. The wind would probably be moving the balloon as the balloonist tried to take these measurements, and it’s unlikely that the two angles could be measured from exactly the same vantage point. The problem also assumes that Groveburg is a flat city, or at least that the elevation of the soccer fields is the same as that of the football field.
And, while not pseudocontext, we have another situation where the author asks the student to solve for inconsequential measurements and ignore the consequential one:
The questions aren’t what you want to know. You want to know how high up the balloon is! It’s not like you can’t figure it out from the info given either. It can be done with the Law of Sines, which is the focus of the lesson.
And then we’re back to the pseudocontext:
If you do calculate the balloon’s height, you find that the balloon is about 1.24 miles above Groveburg, which is also unlikely since an average hot air balloon ride only goes up to 2000 feet.
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measures the angle of depression to the Groveburg soccer fields to be 20° 15′. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62° 30′. The distance between the two athletic complexes is 4 miles.
- Find the distance from the balloon to the soccer fields.
- What is the distance from the balloon to the football field?
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