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Scanning for Mountains


Date: 06/02/99 at 03:09:10
From: Leanne Kwok
Subject: Geometry

Dr. Math,

Hi can you help me with this math question?

I am standing on a hill 600 metres high and scanning the horizon to 
see a mountain 200 km away. High-Tech optical equipment is available. 
How high must the mountain be for this equipment to be any use? Assume 
the radius of the earth is 6360km.

Thank you very much.


Date: 06/02/99 at 11:47:28
From: Doctor Rob
Subject: Re: Geometry

Let the distance from you to the horizon be d km, the radius of the 
earth r km, and the height of the mountain x km. Then by the 
Pythagorean Theorem,

   (r+.6)^2 = d^2 + r^2
          d = sqrt(1.2*r + 0.36).

Now the distance from the horizon to the top of the mountain is 
200 - d km, and by the Pythagorean Theorem again,

   (r+x)^2 = r^2 + (200-d)^2,

Now substituting r = 6360, and solving for x, you get the answer you 
seek.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Practical Geometry

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