Please help on this question!!! An observer in a hot-air balloon sights a building that is 50 m from the balloon’s launch point. The balloon has risen 165 m. What is the angle of depression from the balloon to the building? Round to the nearest degree.

Question

anonymous · Answer

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anonymous · Answer

$$\text{ArcTan}\left[\frac{165}{50}\right]=73 \text{ degrees}$$

anonymous · Answer

thank you! But how to do you come up with 165/50?

anonymous · Answer

The problem text says that the balloon's elevation is 165 meters.
The visible part of the diagram says 65 meters.

anonymous · Answer

I know but how to do you to divide?

anonymous · Answer

*know to divide

anonymous · Answer

According to the diagram, the balloon's nadir is 50 feet from the building.
nadir:   The point on the celestial sphere directly below an observer.

anonymous · Answer

The angle of depression is equal to the angle of elevation from the building.
The angle of the balloon's elevation from the building is the arctan(165/50).

anonymous · Answer

i think i get it... thanks :)

anonymous · Answer

By the way, you may be asked to solve the same type of problem in the future, like the angle of depression from a light house on a cliff to a boat on the water or the edge of a pier to a boat on the water.