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Trigonometry
can be used on a daily basis in the workplace. Since
trigonometry means "triangle measure", any
profession that deals with measurement deals with
trigonometry as well. Carpenters, construction
workers and engineers, for example, must possess a
thorough understanding of trigonometry.
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In
word problems, the formulas remain the same: |
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Word
problems introduce two new vocabulary terms:
| Angle
of Elevation
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The angle
of elevation is always measured from the ground
up. Think of it like an elevator that only goes up. It
is always INSIDE the triangle.
In the diagram at the left, x
marks the angle of elevation of the top of the tree as seen from a
point on the ground.
You can think of the angle of
elevation in relation to the movement of your eyes. You are
looking straight ahead and you must raise (elevate) your eyes to
see the top of the tree. |
| Angle
of Depression
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The angle
of depression is always OUTSIDE
the triangle. It is never inside the triangle.
In the
diagram at the left, x marks the angle of depression of a
boat at sea from the top of a lighthouse.
You can think of the angle of
depression in relation to the movement of your eyes. You are
standing at the top of the lighthouse and you are looking straight
ahead. You must lower (depress) your eyes to see the boat in
the water. |
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As seen in the diagram above of
angle of depression, the
dark black horizontal line is parallel to side CA of triangle
ABC. This forms what are called alternate interior angles which are
equal in measure
(so, x also equals the measure of <BAC).
Simply stated, this means that:
the angle of elevation =
the angle of depression. |
So
what do we do with this angle of depression
that is OUTSIDE of our
triangle?
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There are
two possible ways to use our angle of
depression to obtain an angle INSIDE the triangle.
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find the
angle adjacent (next door) to our angle which is inside the
triangle. This adjacent
angle will always be the complement of our angle. Our
angle and the angle next door will add to 90º. In the
diagram on the left, the adjacent angle is 55º.
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utilize
the fact that the angle of depression
= the angle of elevation and simply place 35º in
angle A. (the
easiest method) Just be sure to place it in
the proper position.
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Once
you have created your diagram, the word problems are solved in exactly the
same manner as the problems we discussed in the lesson
on finding a side and the lesson on finding an
angle.
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See how to use
your
TI-83+/TI-84+ graphing calculator with
beginning trigonometry.
Click calculator. |
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