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Trigonometry Formulas for Area of Triangle
and Area of Parallelogram
The formula for the
area of a triangle is
where b stands for the base and h stands for the altitude
(height)
drawn to that base. |
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(lettering the diagram is of no importance to the
formula) |
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By using trigonometry in the right triangle (on the left
side of the diagram), we find:
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Multiplying by b, gives  .
Substituting this new value of h into the area formula gives the trig area of
triangle formula:
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SAS Formula
for the area of a triangle
where the pattern is to use "two sides and
the sine of the included angle".
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The diagonal of a parallelogram
divides the parallelogram into two congruent triangles.
Consequently, the area of a parallelogram can be thought of as
doubling the area of one of the triangles formed by a diagonal.
This gives the trig area formula for a
parallelogram:
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Example 1:
| Given the triangle at
the right, find its area, to the nearest hundredth.
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Be careful!!! When using your graphing calculator, be
sure that you are in DEGREE Mode,
or that you are using the degree symbol
if in RADIAN Mode. |
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Degree Mode: |
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Radian Mode:
Find degree symbol under
ANGLE (2nd APPS) |
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Example 2:
Given the parallelogram
at the right, find its area to the nearest hundredth.
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Again!!! Be
sure that you are in DEGREE Mode,
or that you are using the degree symbol
if in RADIAN Mode. |
If this problem had asked for an
EXACT answer, do not
use your calculator, as the calculator rounds the value for sin
120º.
It will be necessary to use the 30º- 60º- 90º
reference triangle in Quadrant II. The EXACT ANSWER will
be
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Check to see that the exact answer
yields the calculator decimal answer. |
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