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.