What is the difference in the observed angles between a person standing on a flat surface and a person standing on top of a 10-foot-tall building looking at the same tree?
To determine the difference in the observed angles between a person standing on a flat surface and a person standing on top of a 10-foot-tall building looking at the same tree, we need to understand some basic concepts.
Firstly, let's assume that the tree is some distance away from both the person on the flat surface and the person on top of the building. We'll refer to this distance as "d."
When a person on the flat surface looks at a distant object, they are essentially observing it at eye level, which is parallel to the ground. In this case, the observed angle from the person on the flat surface would be 0 degrees or horizontally parallel to the ground.
On the other hand, the person standing on top of the 10-foot-tall building will have an elevated vantage point. This means that they will observe the tree from an angle slightly above horizontal.
To find the specific angle, we can use simple trigonometry. The tangent of an angle is calculated by dividing the height (10 feet in this case) by the distance (d). Therefore, we have:
Tangent of angle = height / distance
We can rearrange this equation to find the angle:
Angle = arctan(height / distance)
Once you know the specific distance (d), you can plug it into the equation to determine the angle observed by the person on top of the building.
It's important to note that the angle observed will depend on the distance between the tree and the person on top of the building. The closer the person is to the tree, the larger the angle will be. Similarly, if the person is farther away from the tree, the angle will be smaller.
Remember to measure the distance accurately and use the appropriate units, such as feet or meters, when calculating the angle.