Q&A #6237

Teachers' Lounge Discussion: Trigonometry

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From: loyd

To: Teacher2Teacher Public Discussion
Date: 2001072021:34:43
Subject: Re: Trigonometry Uses; edit the last post

I edited to make correction in a couple of places.  I replaced good
with poor in paragraph 4.  The power factor is poor if you push the
sliding door from the side.  I also corrected where I said previously
that the diagonals meet at a corner.  I meant to say  side and
diagonal meet at a corner.  
1.  Three points determine a plane, hence the three legged milk stool
won't rock on an uneven surface.  4 legged table will.

2.  Triangle will hold its shape or else break If you join three
sticks with a nail at each vertex.  Thus, we use triangles for house
building and constructions of all types to make strong structures.
Rectangles will not hold shape if only one nail is used to join the 4
pieces of wood with only one nail at the vertices.  All engineering
courses require a thorough knowledge of trig.

I know a man who built his own house and there were no joists joining
his walls so that it was shaped like this with no triangles:

/  \
|  |

By and by, the walls started spreading apart.  Solution, add joists to
form triangles connected from wall to wall.

3.  Electrical engineering requires trig to understand how motors and
generators work.  The alternating current used in most equipment is a
sinusoid or sine wave.  Trig is required to understand most electrical
engineering problems.  

4.  Mechanical power factor is determined by the cosine of the angle
that is applied to your work.  An example of a poor power factor is
when you push a sliding door from the side at 90 degrees vice 0
degrees.  The door doesn't move unless you have an angle less than 90
degrees - poor power factor when the angle approaches 90.  Electrical
circuits have also have power factor but it is a little more abstract
which makes it exciting.

4.  Squaring a house, or pyramid requires trig (Pythagorean Theorem).
The 6,8 10 triangle is useful here as well as knowing that a rectangle
has diagonals that are equal.  One can use this method by using a
tape, screwdriver and nails to create arcs when building a house. 
Instead of pencil marks, stick nails in the ground, and with the tape
held at the other end by a large screw driver, you can create arcs
with one diagonal and and a side.  Do the same with another diagonal,
and a side on the other end and where the arcs of a side and a
diagonal cross, is another corner. 

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