An Introduction to Trigonometry
Math 101.01
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Have the most careful, neatest people in your group measure A, B, C, a, b, c, , , and
.
It is absolutely essential that you measure these as accurately as possible. I suggest
using millimeters. If you do not measure these accurately, the rest of this worksheet
(and perhaps the rest of this term (rest of your life?)) will not make sense! Before
you decide to be sloppy, you better ask yourself if it's worth it.
1. Record your measurements here:
A = _______________
a = _______________
 = ______________
B = _______________
b = _______________
 = ______________
C = _______________
c = _______________
 = ______________
2. Using your measurements from #1, compute the following:
A2  B 2 = ___________________
C 2  __________________
a 2  b 2  ____________________
c 2  ___________________
 2   2  ___________________
 2  ___________________
Record your observations here (use big words like hypotenuse and sum):
3. Using your measurements from #1, compute the following ratios:
A
 ___________________
B
a
 ___________________
b

 ___________________

4. Compute the following ratios:
A
 ___________________
C
a
 ___________________
c

 ___________________

5. Compute the following ratios:
B
 ___________________
C

 ___________________

Record your observations below:
b
 ___________________
c
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Notice that the angles opposite sides A, a, and  are equal. You can observe this by
placing the triangles on top of each other.
Similarly the angles opposite sides B, b, and  are equal.
Lastly, the angles opposite the sides C, c, and  are equal.
Triangles that have the same set of angles are called "similar triangles" or
"congruent triangles." The 3 triangles you've been given are, therefore, similar
triangles.
Suppose you were given a fourth triangle that is similar to the other three and suppose
further that somebody had written the letters A, B, and C on the triangle on the
appropriate sides. What sort of predictions can you make about A, B, and C? List your
predictions below:
You may have noticed that the 3 triangles you were given are each right triangles (a right
triangle is a triangle in which one of the angles is 90 (in your triangles, the angle
opposite the side labeled C, c, and  is 90)). What do you think would happen if you
hadn't been given right triangles? How many of the results you discussed above do you
think would still be valid? Discuss your feelings below: