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/
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