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### Trigonometry and the Earth

```
Date: 07/13/99 at 00:07:34
From: Mike
Subject: Trigonometry and the Earth

A woman 6 ft. tall stands at the edge of the ocean. The radius of the
earth is 3960 miles. How far out can she see?

Thank you.
```

```
Date: 07/13/99 at 08:44:45
From: Doctor Rick
Subject: Re: Trigonometry and the Earth

Hi, Mike.

In the figure below, the circle is the earth, with center at point O.
The radius OB = OC is 3960 miles. The woman's eye is at point A;
distance AC is 6 feet (I've exaggerated this distance a bit). Line AB
is the line of sight to the horizon; it is tangent to the surface of
the earth, so angle ABO is a right angle.

A
|\
| \
|   \
|    \
|      \
C|       \
******       \
*        |       *  \
*           |          * \
*             |            *\
*               |              * B
*                |             / *
*                 |          /     *
*                  |       /         *
*                   |    /             *
*                   | /                *
*                   O                  *
*                                      *
*                                    *
*                                  *
*                                *
*                              *
*                          *
*                      *
*                *
******

You can figure the distance to the horizon, AB, by using the
Pythagorean theorem.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

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