Answer: The horizontal distance from the hot air balloon to the building is approximately 2533.39 meters.
Explanation:
We can use trigonometry to solve this problem. Let's draw a diagram to visualize the situation!!
=== begin diagram ===
B (balloon)
/|
/ |
/ | 520m
/ |
/θ |
/ |
/______|___ C (ground)
A D
=== end diagram ===
In the diagram, we have a hot air balloon at point B that is 520m from the ground at point C. We also have a building at point D that is 450m tall. The angle of elevation from point D to point B is 10 degrees (angle θ).
We want to find the horizontal distance between point B and point D (distance AB in the diagram).
To do this, we can use the tangent function:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the building (450m) and the adjacent side is the horizontal distance we want to find (AB). We can rearrange the formula to solve for AB:
AB = opposite/tan(θ)
AB = 450m / tan(10°)
AB ≈ 2533.39m
Therefore, the horizontal distance from the hot air balloon to the building is approximately 2533.39 meters.