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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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