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From a hot-air balloon, Jace measures a 31° angle of depression to a landmark that's

331 feet away, measuring horizontally. What's the balloon's vertical distance above

the ground? Round your answer to the nearest hundredth of a foot if necessary.

1 Answer

2 votes

Answer:

Balloon's vertical distance = 198.88 feet

Explanation:

  • For these kinds of problems, it's best to draw a mini diagram and I'll attach a diagram I used while working through the problem.

The mention of an angle of depression is a clue indicating that we'll be working with a right triangle.

The sides of the right triangle consist of:

  • The balloon's vertical distance,
  • the landmark's horizontal distance,
  • and the diagonal distance between the hot air balloon and the landmark create a right triangle.

Because we have a right triangle, we can find the balloon's vertical distance using one of the trigonometric ratios.

When the 31° angle is the reference angle:

  • the balloon's vertical distance (let's call it v) is the opposite side,
  • and the landmark's horizontal distance (let's call it v) is the adjacent side.

Thus, we can use the tangent ratio, whose general equation is:

tan (θ) = opposite/adjacent, where

  • θ is the reference angle.

Thus, we can find v, the balloon's vertical distance above the ground rounded to the nearest hundredth, by plugging in 31 for θ and 331 for the adjacent side side:

(tan (31) = v/331) * 331

331 * tan (31) = 331

v = 331 / tan (31)

v = 198.8848649

v = 198.88

Thus, the balloon's vertical distance above the ground is about 198.88 feet.

User Anael
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