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Date: 06/08/2000 at 05:56:24
From: Amy Vyse Widdicombe
Subject: Bearings

We have to teach a math lesson for one hour about bearings, and we
don't have a clue as to what bearings are. We have to locate a point
using two bearings. Also, can you think of any activities to entertain
the class instead of making it a boring lesson? We want it to be fun.

Help us; we don't know what to do.
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Date: 06/08/2000 at 13:04:02
From: Doctor Rick
Subject: Re: Bearings

Hi, Amy.

First of all, a bearing is a compass direction. That is, it's the
angle between north and the line between two objects. The bearing from
where you are (point P) to some object (point A) is the angle between
a line going north from point P, and the line from point P to point A.

If you're in geometry class, then the ability to locate a point P
using bearings to two points A and B is a consequence of the
angle-side-angle congruence theorem. The bearings aren't the same as
the angles of the triangle, but if you know the bearing from point A
to point B, as well as the bearings from point P to points A and B,
you can find all the angles of the triangle ABP. You'll want to expand
on these concepts.

So much for the blackboard explanation. There's lots of room for
making this fun, and no excuse for a boring lesson! The best way would
be to hold the class outdoors and have some games in which you look
for "buried treasure" where the clues are the bearings from two trees
to the treasure. You'll need to get hold of at least one magnetic
compass. By the way, you can make up the clues by standing at the
"treasure" and taking bearings to the two trees. How are these
bearings related to the bearings from the trees to the treasure? You
must be sure you know which way the bearings go.

If you have to be in class, you could have a student leave the room
or be blindfolded, then choose another student to take bearings from
his/her seat to two corners of the room. Then the first student comes
in or takes the blindfold off, and tries to determine which student
you chose, using the bearings the chosen student measured.

You'll want to give some training in using a compass before you do any
games. If you have to be indoors, some odd things might happen if
there is a lot of metal in the room.

Here are some Web sites I've found that may give you some ideas:

Conning and Pilotage - John Jacq
(how to find where you are in a boat)
http://www.axs.com.au/~jjjacq/sundry/navconn.html

Map and Compass - Search and Rescue Society of British Columbia
http://www.sarbc.org/m&c.html

Measuring Distances-Triangulation - Explorer lesson plan
http://explorer.scrtec.org/explorer/explorer-db/html/783751625-447DED81.html

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Geometry
High School Practical Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Terms/Units of Measurement
Middle School Triangles and Other Polygons

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