# Calculating Height of a Mountain: Is It Possible?

• dragonblood
In summary: It is not necessary to know the actual distances between the locations. In summary, using the angles and heights of the two mountains, you can deduce your altitude above the ocean without knowing any distances between the locations.
dragonblood
I apologize if this problem is more of a math- than a physics problem. At least it is applicable in real life :)

You are standing on some mountain and in your view are two other mountains, A and B. Also you can see the ocean as a referance zero point. The height of both mountains A and B are given.

You are blessed with tools allowing you to measure angles accurately between, say the two mountains, between the reference point and either mountain, and so on.

You unfortunately do not know any distances between any of the locations.

The question is: are you able to deduce the altitude in which you are positioned? That is, how high above the ocean are you?

I'm not sure if you have sufficient knowledge to determine this, or if at least one distance is required.

Thank you so much in advance :)

Yes, you can determine your altitude based on the angles and heights of the two mountains. The key is to draw a triangle connecting the three points (you, mountain A, and mountain B). Then, you can use the law of sines or the law of cosines to calculate the distances between the three points and then calculate the altitude using the height of the two mountains.

## 1. How do scientists calculate the height of a mountain?

Scientists use a variety of methods to calculate the height of a mountain, including satellite imagery, aerial photography, and ground-based measurements using tools such as altimeters and theodolites. These measurements are then combined and compared to known elevations in the surrounding area to determine the mountain's height.

## 2. Is it possible to accurately calculate the height of a mountain?

Yes, it is possible to accurately calculate the height of a mountain using modern technology and precise measurement techniques. However, factors such as weather conditions and the mountain's geological features can make it challenging to obtain an exact measurement.

## 3. What is the most accurate method for calculating the height of a mountain?

The most accurate method for calculating the height of a mountain is using ground-based measurements with specialized tools, as this allows for direct measurement of the mountain's elevation. However, this method can be time-consuming and may not be feasible for remote or inaccessible mountains.

## 4. Can the height of a mountain change over time?

Yes, the height of a mountain can change over time due to geological processes such as erosion or tectonic activity. However, these changes are typically gradual and may not be noticeable in the span of a human lifetime.

## 5. Are there any limitations to calculating the height of a mountain?

There are a few limitations to calculating the height of a mountain, such as weather conditions or technical difficulties in obtaining accurate measurements. Additionally, some mountains may have varying heights depending on which point is measured, making it challenging to determine a single height for the entire mountain.

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