Real Numbers And The Pythagorean Theorem Worksheet - Chapter 7 Page 17
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46Lesson
7.3
Lesson Tutorials
Key Vocabulary
theorem, p. 300
Sides of a Right Triangle
legs, p. 302
The sides of a right triangle have special names.
hypotenuse, p. 302
Pythagorean
Theorem, p. 302
The hypotenuse
hypotenuse, c
leg, a
is the side opposite
the right angle.
The legs are the
two sides that form
leg, b
the right angle.
Study Tip
The Pythagorean Theorem
In a right triangle,
In any right triangle, the sum of the squares of the
Words
the legs are the
lengths of the legs is equal to the square of the length
shorter sides and the
of the hypotenuse.
hypotenuse is always
the longest side.
2
+
2
=
2
b
c
a
Algebra
Finding the Length of a Hypotenuse
1 1
EXAMPLE
Find the length of the hypotenuse of the triangle.
5 m
2
+
2
=
2
a
b
c
Write the Pythagorean Theorem.
2
+
2
=
2
5
12
c
Substitute 5 for a and 12 for b.
25 + 144 = c
2
Evaluate powers.
c
12 m
169 = c
2
Add.
—
—
√
√
169 =
2
c
Take positive square root of each side.
13 = c
Simplify.
The length of the hypotenuse is 13 meters.
Find the length of the hypotenuse of the triangle.
2.
3
Exercises 3 and 4
1.
in.
10
c
8 ft
2
in.
c
5
15 ft
302
Chapter 7
Real Numbers and the Pythagorean Theorem
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