Final answer:
To find the distance to the landing site, we use the trigonometric function tangent, where the angle of elevation is equal to the angle of depression and is given as 17°. Tan(17°) = 1208 / distance, leading to a distance of approximately 4052 meters to the landing site.
Step-by-step explanation:
To find the distance to the landing site from the balloon when the balloonist's altitude is 1208 meters, and the angle of depression is 17 degrees, we can use trigonometry. The angle of depression corresponds to the angle of elevation from the landing site to the balloon, given the two are alternate interior angles and thus equal.
We can use the tangent function since we have the opposite side (altitude) and we want to find the adjacent side (distance to the landing site). The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side.
Therefore, we use the formula:
- tan(∠) = opposite/adjacent
Substituting the values we have:
From this, the distance can be calculated as:
- distance = 1208 / tan(17°)
We use a calculator to find this distance and round to the nearest meter as the question asks:
The landing site is therefore approximately 4052 meters away from the balloon to the nearest meter.