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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?  

Please help me out with this one!  
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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