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Involving Angles | Pythagorean Theorem
Pythagorean Theorem
 Before we leave basic formulas, we will consider a basic formula (or Theorem)
which is widely used in mathematics. It is called the Pythagorean Theorem.
The Pythagorean (pith-ag'-or-ean) Theorem is named after the man who proved
it, Pythagoras (pith-ag'-or-us). It establishes relationships among the sides
of a right triangle. Remember, It applies only to RIGHT triangles.
In any right triangle, such as the one in Figure 21, it is always
true that a2 + b2 =
c2 where c
is the
length of the hypotenuse and a
and
b are the lengths of the two sides.
The hypotenuse is the side opposite the right angle (side c in Figure
21).
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Figure 21 - A right triangle
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| We can use this theorem to
calculate measurements. For example, if we wanted to determine the
distance across a lake or other obstacle where we were unable to ue a tape
measure (see Figure 22), we could measure a distance (AB), turn a 90° angle, and
measure another distance (AB). Then we would be able to calculate the
distance across the lake (AB) since:
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|
c2 =
a2
+ b2 |
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then |
c2 =
32 + 42 |
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and |
c2 =
9 + 16 |
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c2 = 25 |
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c =
= 5
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Figure 22
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Here is another example where the use of the Pythagorean Theorem is
helpful. Suppose you needed to get a ladder to reach the top of
your 12 foot high house and it had to stand
5 feet from the house.
What size ladder would you get? See Figure 23.
As you now know, the theorem says:
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|
c2 =
a2
+ b2 |
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c2
= 122 + 52 |
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c2 = 144 + 25
= 169 |
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c =
= 13 ft. |
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Figure 23 |
You now know you need to get a 13 ft. ladder.
Now, let's stop and take Practice
Exercise 9-6. (top)
Go to this website for some
interactive demonstrations of the Pythagorean Theorem: www.ies.co.jp/math/java/geo/pythagoras.html.
Step by step solutions to some of the Practice Exercises are provided when
you click on the math link below:
http://www.mathgoodies.com/lessons/vol1/solutions_vol1.html
Next Page: Lesson 9
Problems
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