Calculating Height of a Mountain: Is It Possible?

[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 :)

 

[Valerie Park]

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.