Answer:
960.50 feet
Explanation:
You want to know the height of a balloon if it is 1424 feet horizontally from a landmark at an angle of depression of 34°.
Tangent
The geometry of the problem can be modeled as a right triangle with a base angle of 34°, the adjacent leg 1424 feet, and the opposite leg being the height of the balloon. The tangent relation tells us ...
Tan = Opposite/Adjacent
Opposite = Adjacent·Tan
height = (1424 feet)·tan(34°) ≈ 960.50 feet
The balloon's vertical distance from the ground is 960.50 feet.
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Additional comment
If the angle is measured to the nearest degree, then the height of the balloon is somewhere between 943 feet and 979 feet. The only purpose served by reporting the distance to the nearest 0.01 foot is to see if you can use your calculator correctly.
To make that precision for the height meaningful, the angle would need to be measured with an error less than 0.00014°, about 1/2 arc-second. This is better resolution than the best surveying instruments offer, by a factor of about 30.
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